\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 (\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a)<\/title>\n<style>\n :root{\n --brand:#bdb76b; \/* \u0630\u0647\u0628\u064a \u0641\u0627\u062a\u062d *\/\n --ink:#0f172a;\n --sub:#475569;\n --muted:#64748b;\n --chip:#f8fafc;\n --note:#fffbea;\n --note-b:#fde68a;\n --tips:#f0fdf4;\n --tips-b:#bbf7d0;\n --warn:#fff1f2;\n --warn-b:#fecdd3;\n }\n html,body{background:#ffffff; color:#111; font-family:\"Segoe UI\",Tahoma,Arial,sans-serif; line-height:1.9; margin:0}\n article{max-width:980px; margin:24px auto; padding:24px}\n h1,h2,h3{color:var(--ink); margin:1.2em 0 .5em}\n h1{font-size:32px} h2{font-size:24px} h3{font-size:19px}\n p{margin:.8em 0}\n .sub{color:var(--sub)}\n .pill{display:inline-block; padding:.2em .6em; border-radius:999px; background:var(--brand); color:#111; font-weight:700; font-size:12px; margin-left:6px}\n .toc{background:var(--chip); border:1px solid #e2e8f0; border-radius:14px; padding:14px 16px}\n .toc a{color:#111; text-decoration:none}\n .toc ol{margin:.5em 1.2em}\n .note{background:var(--note); border:1px solid var(--note-b); border-radius:12px; padding:12px 14px}\n .tips{background:var(--tips); border:1px solid var(--tips-b); border-radius:12px; padding:12px 14px}\n .warn{background:var(--warn); border:1px solid var(--warn-b); border-radius:12px; padding:12px 14px}\n .grid{display:grid; gap:12px}\n .g2{grid-template-columns:repeat(2,minmax(0,1fr))}\n .g3{grid-template-columns:repeat(3,minmax(0,1fr))}\n @media(max-width:900px){ .g3{grid-template-columns:1fr} }\n @media(max-width:800px){ .g2{grid-template-columns:1fr} }\n figure{margin:16px auto; text-align:center}\n figcaption{font-size:13px; color:var(--muted)}\n table{border-collapse:collapse; width:100%; margin:14px 0; font-size:15px}\n th,td{border:1px solid #e5e7eb; padding:8px 10px; text-align:right}\n th{background:#f8fafc}\n code.kbd{font-family:ui-monospace,Menlo,monospace; background:#f1f5f9; padding:2px 6px; border-radius:6px}\n .badge{background:#f1f5f9; border:1px dashed var(--brand); border-radius:10px; padding:.3em .6em; font-size:12px; color:#111}\n details{background:#f8fafc; border:1px solid #e2e8f0; padding:10px 12px; border-radius:12px; margin:10px 0}\n summary{cursor:pointer; font-weight:700}\n .cta{background:#eef2ff; border:1px solid #c7d2fe; border-radius:12px; padding:12px 14px}\n .foot{color:var(--muted); font-size:13px; margin-top:28px}\n .tag{background:#e2e8f0; color:#111; border-radius:8px; padding:.1em .5em; font-size:12px; margin-left:6px}\n .hr{height:1px; background:#e2e8f0; margin:18px 0}\n<\/style>\n<\/head>\n<body>\n<article>\n <header>\n <h1>\ud83d\udcd0 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 <span class=\"pill\">\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a<\/span><\/h1>\n <p class=\"sub\">\u0645\u0631\u062c\u0639 \u0634\u0627\u0645\u0644 \u064a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u0641\u0647\u0645 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u0648\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0634\u0628\u0643\u0629.<\/p>\n <\/header>\n\n <section class=\"toc\">\n <strong>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/strong>\n <ol>\n <li><a href=\"#objectives\">\ud83c\udfaf \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0651\u0645 \u0648\u0627\u0644\u0645\u062a\u0637\u0644\u0628\u0627\u062a<\/a><\/li>\n <li><a href=\"#plane\">\ud83d\uddfa\ufe0f \u0645\u0631\u0627\u062c\u0639\u0629 \u0633\u0631\u064a\u0639\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0627\u0644\u0645\u062d\u0627\u0648\u0631<\/a><\/li>\n <li><a href=\"#slope\">\ud83d\udcc8 \u0627\u0644\u0645\u064a\u0644: \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u062a\u0641\u0633\u064a\u0631<\/a><\/li>\n <li><a href=\"#equations\">\u270d\ufe0f \u0635\u064a\u063a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 (\u0645\u064a\u0644-\u0645\u0642\u0637\u0639\u060c \u0646\u0642\u0637\u0629-\u0645\u064a\u0644\u060c \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629)<\/a><\/li>\n <li><a href=\"#parallel\">\u2194\ufe0f \u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0648\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/a><\/li>\n <li><a href=\"#distance-midpoint\">\ud83d\udccf \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629<\/a><\/li>\n <li><a href=\"#models\">\ud83e\udde9 \u0645\u0633\u0627\u0626\u0644 \u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0645\u0646 \u0627\u0644\u0648\u0627\u0642\u0639<\/a><\/li>\n <li><a href=\"#practice\">\ud83d\udcdd 20 \u062a\u0645\u0631\u064a\u0646\u064b\u0627 \u0645\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0645\u062e\u062a\u0635\u0631\u0629<\/a><\/li>\n <li><a href=\"#mistakes\">\u26a0\ufe0f \u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629 + \u0646\u0635\u0627\u0626\u062d \u0627\u0644\u0645\u0630\u0627\u0643\u0631\u0629<\/a><\/li>\n <li><a href=\"#cheatsheet\">\ud83d\udcce \u0645\u0644\u062e\u0635 \u0633\u0631\u064a\u0639 (Cheat Sheet)<\/a><\/li>\n <\/ol>\n <\/section>\n\n <section id=\"objectives\">\n <h2>\ud83c\udfaf \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0651\u0645 \u0648\u0627\u0644\u0645\u062a\u0637\u0644\u0628\u0627\u062a<\/h2>\n <div class=\"grid g2\">\n <div class=\"tips\">\n <strong>\u0633\u062a\u062a\u0639\u0644\u0645 \u0623\u0646:<\/strong>\n <ul>\n <li>\u062a\u062d\u0633\u0628 \u0627\u0644\u0645\u064a\u0644 \u0648\u062a\u0641\u0633\u0631\u0647 \u0643\u0640 <em>\u0645\u0639\u062f\u0644 \u062a\u063a\u064a\u0651\u0631<\/em>.<\/li>\n <li>\u062a\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0633\u062a\u0642\u064a\u0645 \u0628\u0623\u0643\u062b\u0631 \u0645\u0646 \u0635\u064a\u063a\u0629 \u0648\u062a\u062d\u0648\u0651\u0644 \u0628\u064a\u0646\u0647\u0627.<\/li>\n <li>\u062a\u062c\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641 \u0628\u062f\u0642\u0629.<\/li>\n <li>\u062a\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0632\u064a \u0648\u0627\u0644\u062a\u0639\u0627\u0645\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u064a\u0644.<\/li>\n <\/ul>\n <\/div>\n <div class=\"note\">\n <strong>\u0645\u0631\u0627\u062c\u0639\u0629 \u0644\u0627\u0632\u0645\u0629:<\/strong>\n <ul>\n <li>\u062a\u0631\u062a\u064a\u0628 \u0623\u0632\u0648\u0627\u062c: <code class=\"kbd\">(x,y)<\/code> \u0648\u062a\u062d\u062f\u064a\u062f \u0631\u0628\u0639 \u0627\u0644\u0646\u0642\u0637\u0629.<\/li>\n <li>\u0639\u0645\u0644\u064a\u0627\u062a \u062c\u0628\u0631\u064a\u0629 \u0623\u0633\u0627\u0633\u064a\u0629.<\/li>\n <\/ul>\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"plane\">\n <h2>\ud83d\uddfa\ufe0f \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a<\/h2>\n <p>\u064a\u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u062d\u0648\u0631\u0627\u0646 <code class=\"kbd\">x<\/code> \u0648 <code class=\"kbd\">y<\/code> \u0639\u0646\u062f \u0627\u0644\u0623\u0635\u0644 <code class=\"kbd\">(0,0)<\/code>\u060c \u0648\u062a\u0642\u0633\u0645 \u0627\u0644\u0645\u0633\u062a\u0648\u064a \u0625\u0644\u0649 \u0623\u0631\u0628\u0639\u0629 \u0623\u0631\u0628\u0627\u0639. \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u062a\u062d\u062f\u062f \u0627\u0644\u0631\u0628\u0639.<\/p>\n <div class=\"grid g2\">\n <div>\n <h3>\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0631\u0628\u0639<\/h3>\n <ul>\n <li><strong>\u0627\u0644\u0631\u0628\u0639 \u0627\u0644\u0623\u0648\u0644:<\/strong> <code class=\"kbd\">(+,+)<\/code><\/li>\n <li><strong>\u0627\u0644\u062b\u0627\u0646\u064a:<\/strong> <code class=\"kbd\">(\u2212,+)<\/code><\/li>\n <li><strong>\u0627\u0644\u062b\u0627\u0644\u062b:<\/strong> <code class=\"kbd\">(\u2212,\u2212)<\/code><\/li>\n <li><strong>\u0627\u0644\u0631\u0627\u0628\u0639:<\/strong> <code class=\"kbd\">(+,\u2212)<\/code><\/li>\n <\/ul>\n <\/div>\n <div class=\"tips\">\n <strong>\u0645\u062b\u0627\u0644 \u0633\u0631\u064a\u0639:<\/strong> \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(\u22123,4)<\/code> \u062a\u0642\u0639 \u0641\u064a \u0627\u0644\u0631\u0628\u0639 \u0627\u0644\u062b\u0627\u0646\u064a\u061b \u0644\u0623\u0646\u0647\u0627 \u0633\u0627\u0644\u0628\u0629 \u0639\u0644\u0649 <code class=\"kbd\">x<\/code> \u0648\u0645\u0648\u062c\u0628\u0629 \u0639\u0644\u0649 <code class=\"kbd\">y<\/code>.\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"slope\">\n <h2>\ud83d\udcc8 \u0627\u0644\u0645\u064a\u0644: \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u062a\u0641\u0633\u064a\u0631<\/h2>\n <p><strong>\u0627\u0644\u0645\u064a\u0644<\/strong> \u064a\u0633\u0627\u0648\u064a \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u062a\u063a\u064a\u0651\u0631 \u0627\u0644\u0631\u0623\u0633\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u063a\u064a\u0651\u0631 \u0627\u0644\u0623\u0641\u0642\u064a: <code class=\"kbd\">m = (y2 \u2212 y1) \/ (x2 \u2212 x1)<\/code>. \u064a\u0645\u062b\u0651\u0644 <em>\u0645\u062f\u0649 \u0627\u0631\u062a\u0641\u0627\u0639<\/em> \u0627\u0644\u062e\u0637 \u0644\u0643\u0644 \u062e\u0637\u0648\u0629 \u064a\u0645\u064a\u0646\u064b\u0627.<\/p>\n <div class=\"grid g2\">\n <div>\n <h3>\u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u0645\u064a\u0644<\/h3>\n <ul>\n <li><span class=\"badge\">\u0645\u0648\u062c\u0628<\/span>: \u0627\u0644\u062e\u0637 \u064a\u0635\u0639\u062f \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u0625\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646.<\/li>\n <li><span class=\"badge\">\u0633\u0627\u0644\u0628<\/span>: \u0627\u0644\u062e\u0637 \u064a\u0647\u0628\u0637.<\/li>\n <li><span class=\"badge\">\u0635\u0641\u0631<\/span>: \u062e\u0637 \u0623\u0641\u0642\u064a.<\/li>\n <li><span class=\"badge\">\u063a\u064a\u0631 \u0645\u0639\u0631\u0651\u0641<\/span>: \u062e\u0637 \u0631\u0623\u0633\u064a (\u062a\u0642\u0633\u064a\u0645 \u0639\u0644\u0649 \u0635\u0641\u0631).<\/li>\n <\/ul>\n <\/div>\n <div>\n <h3>\u0645\u062b\u0627\u0644 1 (\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u064a\u0644)<\/h3>\n <p>\u0644\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <code class=\"kbd\">A(\u22122,1)<\/code> \u0648 <code class=\"kbd\">B(4,7)<\/code>:<\/p>\n <p><code class=\"kbd\">m = (7 \u2212 1) \/ (4 \u2212 (\u22122)) = 6 \/ 6 = 1<\/code>.<\/p>\n <\/div>\n <\/div>\n\n <h3>\u0645\u062b\u0627\u0644 2 (\u0645\u064a\u0644 \u0645\u0646 \u062c\u062f\u0648\u0644 \u0642\u064a\u0645)<\/h3>\n <table>\n <thead><tr><th>x<\/th><th>y<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>0<\/td><td>2<\/td><\/tr>\n <tr><td>3<\/td><td>8<\/td><\/tr>\n <\/tbody>\n <\/table>\n <p><code class=\"kbd\">m = (8 \u2212 2) \/ (3 \u2212 0) = 6\/3 = 2<\/code>.<\/p>\n <\/section>\n\n <section id=\"equations\">\n <h2>\u270d\ufe0f \u0635\u064a\u063a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645<\/h2>\n <div class=\"grid g2\">\n <div>\n <h3>1) \u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/h3>\n <p><code class=\"kbd\">y = mx + b<\/code> \u062d\u064a\u062b <span class=\"badge\">m<\/span> \u0627\u0644\u0645\u064a\u0644 \u0648 <span class=\"badge\">b<\/span> \u062a\u0642\u0627\u0637\u0639 <code class=\"kbd\">y<\/code>.<\/p>\n <\/div>\n <div>\n <h3>2) \u0646\u0642\u0637\u0629-\u0645\u064a\u0644<\/h3>\n <p><code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code> \u0645\u0641\u064a\u062f\u0629 \u0639\u0646\u062f \u0645\u0639\u0631\u0641\u0629 \u0646\u0642\u0637\u0629 \u0648\u0627\u0644\u0645\u064a\u0644.<\/p>\n <\/div>\n <\/div>\n <h3>3) \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629<\/h3>\n <p><code class=\"kbd\">Ax + By + C = 0<\/code> \u0645\u0639 <code class=\"kbd\">A,B<\/code> \u0644\u064a\u0633\u0627 \u0643\u0644\u0627\u0647\u0645\u0627 \u0635\u0641\u0631\u064b\u0627. \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0628\u064a\u0646 \u0627\u0644\u0635\u064a\u063a \u0628\u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0648\u0627\u0644\u062c\u0645\u0639.<\/p>\n\n <h3>\u0645\u062b\u0627\u0644 3 (\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0645\u064a\u0644)<\/h3>\n <p>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(2,\u22121)<\/code> \u0648\u0645\u064a\u0644\u0647 <code class=\"kbd\">3<\/code>:<\/p>\n <ol>\n <li><code class=\"kbd\">y \u2212 (\u22121) = 3(x \u2212 2)<\/code> \u21d2 <code class=\"kbd\">y + 1 = 3x \u2212 6<\/code>.<\/li>\n <li><code class=\"kbd\">y = 3x \u2212 7<\/code>.<\/li>\n <\/ol>\n\n <h3>\u0645\u062b\u0627\u0644 4 (\u0645\u0646 \u0646\u0642\u0637\u062a\u064a\u0646)<\/h3>\n <p>\u0627\u0644\u0646\u0642\u0637\u062a\u0627\u0646 <code class=\"kbd\">A(1,4)<\/code> \u0648 <code class=\"kbd\">B(5,\u22122)<\/code>:<\/p>\n <ol>\n <li>\u0627\u0644\u0645\u064a\u0644: <code class=\"kbd\">m = (\u22122 \u2212 4)\/(5 \u2212 1) = \u22126\/4 = \u22123\/2<\/code>.<\/li>\n <li>\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0642\u0637\u0629-\u0645\u064a\u0644 \u0645\u0639 <code class=\"kbd\">A<\/code>: <code class=\"kbd\">y \u2212 4 = (\u22123\/2)(x \u2212 1)<\/code> \u21d2 <code class=\"kbd\">y = (\u22123\/2)x + 3\/2 + 4 = (\u22123\/2)x + 11\/2<\/code>.<\/li>\n <\/ol>\n\n <h3>\u062c\u062f\u0648\u0644 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0633\u0631\u064a\u0639<\/h3>\n <table>\n <thead><tr><th>\u0645\u0646<\/th><th>\u0625\u0644\u0649<\/th><th>\u0627\u0644\u062e\u0637\u0648\u0627\u062a<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>\u0646\u0642\u0637\u0629 + \u0645\u064a\u0644<\/td><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u0627\u0633\u062a\u062e\u062f\u0645 <code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code> \u062b\u0645 \u0628\u0633\u0651\u0637 \u0625\u0644\u0649 <code class=\"kbd\">y = mx + b<\/code>.<\/td><\/tr>\n <tr><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u0639\u0627\u0645\u0651\u0629<\/td><td>\u0627\u0646\u0642\u0644 \u0627\u0644\u062d\u062f\u0648\u062f \u0644\u062c\u0647\u0629 \u0648\u0627\u062d\u062f\u0629 \u062b\u0645 \u0631\u062a\u0651\u0628: <code class=\"kbd\">mx \u2212 y + b = 0<\/code>.<\/td><\/tr>\n <tr><td>\u0639\u0627\u0645\u0651\u0629<\/td><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0640 <code class=\"kbd\">y<\/code>: <code class=\"kbd\">y = (\u2212A\/B)x \u2212 C\/B<\/code> (\u0625\u0630\u0627 <code class=\"kbd\">B\u22600<\/code>).<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/section>\n\n <section id=\"parallel\">\n <h2>\u2194\ufe0f \u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0648\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/h2>\n <ul>\n <li><strong>\u0627\u0644\u062a\u0648\u0627\u0632\u064a:<\/strong> \u062e\u0637\u0651\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646 \u0644\u0647\u0645\u0627 \u0627\u0644\u0645\u064a\u0644 \u0646\u0641\u0633\u0647 <code class=\"kbd\">m_1 = m_2<\/code> (\u0645\u0639 \u0627\u062e\u062a\u0644\u0627\u0641 <code class=\"kbd\">b<\/code>).<\/li>\n <li><strong>\u0627\u0644\u062a\u0639\u0627\u0645\u062f:<\/strong> \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u064a\u0644\u064a\u0647\u0645\u0627 <code class=\"kbd\">m_1 \u00b7 m_2 = \u22121<\/code> \u21d2 <code class=\"kbd\">m_2 = \u22121\/m_1<\/code> (\u0627\u0644\u0645\u064a\u0644 \u0627\u0644\u0633\u0627\u0644\u0628 \u0627\u0644\u0645\u0642\u0644\u0648\u0628).<\/li>\n <\/ul>\n <h3>\u0645\u062b\u0627\u0644 5 (\u0645\u0648\u0627\u0632\u064d)<\/h3>\n <p>\u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u0648\u0627\u0632\u064d \u0644\u0640 <code class=\"kbd\">y = 2x + 1<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(0,\u22123)<\/code> \u0647\u064a <code class=\"kbd\">y = 2x \u2212 3<\/code>.<\/p>\n <h3>\u0645\u062b\u0627\u0644 6 (\u0639\u0645\u0648\u062f\u064a)<\/h3>\n <p>\u062e\u0637 \u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 <code class=\"kbd\">y = (1\/2)x \u2212 4<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(2,1)<\/code> \u0644\u0647 \u0645\u064a\u0644 <code class=\"kbd\">m = \u22122<\/code> \u21d2 <code class=\"kbd\">y \u2212 1 = \u22122(x \u2212 2)<\/code> \u21d2 <code class=\"kbd\">y = \u22122x + 5<\/code>.<\/p>\n <\/section>\n\n <section id=\"distance-midpoint\">\n <h2>\ud83d\udccf \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641<\/h2>\n <div class=\"grid g2\">\n <div>\n <h3>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646<\/h3>\n <p><code class=\"kbd\">AB = \u221a[(x2 \u2212 x1)^2 + (y2 \u2212 y1)^2]<\/code> (\u0646\u0627\u062a\u062c\u0629 \u0645\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633).<\/p>\n <h4>\u0645\u062b\u0627\u0644 7<\/h4>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 <code class=\"kbd\">A(\u22121,2)<\/code> \u0648 <code class=\"kbd\">B(3,\u22124)<\/code>:<\/p>\n <p><code class=\"kbd\">AB = \u221a[(3 \u2212 (\u22121))^2 + (\u22124 \u2212 2)^2] = \u221a[4^2 + (\u22126)^2] = \u221a(16+36) = \u221a52 \u2248 7.211<\/code>.<\/p>\n <\/div>\n <div>\n <h3>\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629<\/h3>\n <p><code class=\"kbd\">M = ( (x1 + x2)\/2 , (y1 + y2)\/2 )<\/code>.<\/p>\n <h4>\u0645\u062b\u0627\u0644 8<\/h4>\n <p>\u0645\u0646\u062a\u0635\u0641 <code class=\"kbd\">A(\u22121,2)<\/code> \u0648 <code class=\"kbd\">B(3,\u22124)<\/code> \u0647\u0648 <code class=\"kbd\">M(1, \u22121)<\/code>.<\/p>\n <\/div>\n <\/div>\n\n <h3>\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0639\u0646 \u0645\u0633\u062a\u0642\u064a\u0645 (\u0627\u062e\u062a\u064a\u0627\u0631\u064a \u0645\u062a\u0642\u062f\u0651\u0645)<\/h3>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 <code class=\"kbd\">(x0,y0)<\/code> \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 <code class=\"kbd\">Ax + By + C = 0<\/code> \u0647\u064a <code class=\"kbd\">d = |Ax0 + By0 + C| \/ \u221a(A^2 + B^2)<\/code>.<\/p>\n <\/section>\n\n <section id=\"models\">\n <h2>\ud83e\udde9 \u0645\u0633\u0627\u0626\u0644 \u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0645\u0646 \u0627\u0644\u0648\u0627\u0642\u0639<\/h2>\n <h3>\u0645\u062b\u0627\u0644 9 (\u062a\u0643\u0644\u0641\u0629 \u0648\u062a\u063a\u064a\u0651\u0631 \u062b\u0627\u0628\u062a)<\/h3>\n <p>\u062a\u0643\u0644\u0641\u0629 \u0627\u0634\u062a\u0631\u0627\u0643 \u0625\u0646\u062a\u0631\u0646\u062a: 5 \u062f\u0646\u0627\u0646\u064a\u0631 \u062b\u0627\u0628\u062a\u0629 + 0.8 \u062f\u064a\u0646\u0627\u0631 \u0644\u0643\u0644 \u062c\u064a\u062c\u0627\u0628\u0627\u064a\u062a \u0645\u0633\u062a\u062e\u062f\u0645\u0629. \u0627\u0644\u0646\u0645\u0648\u0630\u062c: <code class=\"kbd\">C(x) = 5 + 0.8x<\/code>. \u0627\u0644\u0645\u064a\u0644 0.8 \u064a\u0639\u0646\u064a \u0632\u064a\u0627\u062f\u0629 0.8 \u062f\u064a\u0646\u0627\u0631 \u0644\u0643\u0644 1 \u062c\u064a\u062c\u0627\u0628\u0627\u064a\u062a.<\/p>\n <h3>\u0645\u062b\u0627\u0644 10 (\u062e\u0631\u064a\u0637\u0629 \u0648\u0645\u0633\u0627\u0641\u0629)<\/h3>\n <p>\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062f\u0631\u0633\u0629 <code class=\"kbd\">S(2,3)<\/code> \u0648\u0627\u0644\u0628\u064a\u062a <code class=\"kbd\">H(\u22124,0)<\/code>. \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 <code class=\"kbd\">\u221a[(\u22126)^2 + (\u22123)^2] = \u221a45 \u2248 6.708<\/code> \u0648\u062d\u062f\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u062e\u0631\u064a\u0637\u0629.<\/p>\n <\/section>\n\n <section id=\"practice\">\n <h2>\ud83d\udcdd 20 \u062a\u0645\u0631\u064a\u0646\u064b\u0627 \u0645\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0645\u062e\u062a\u0635\u0631\u0629<\/h2>\n <ol>\n <li>\u0623\u0648\u062c\u062f \u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0648\u0627\u0635\u0644 \u0628\u064a\u0646 <code class=\"kbd\">(\u22123,5)<\/code> \u0648 <code class=\"kbd\">(1,\u22127)<\/code>.<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0627\u0644\u0645\u0627\u0631 \u0628\u0640 <code class=\"kbd\">(0,4)<\/code> \u0648\u0645\u064a\u0644\u0647 <code class=\"kbd\">\u22123<\/code>.<\/li>\n <li>\u0647\u0644 \u0627\u0644\u062e\u0637 <code class=\"kbd\">2x \u2212 4y + 8 = 0<\/code> \u0645\u0648\u0627\u0632\u064a \u0644\u0640 <code class=\"kbd\">y = (1\/2)x \u2212 1<\/code>\u061f<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 <code class=\"kbd\">y = \u2212(2\/3)x + 1<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(\u22123,2)<\/code>.<\/li>\n <li>\u062d\u0648\u0651\u0644 <code class=\"kbd\">3x + 2y \u2212 10 = 0<\/code> \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u064a\u0644-\u0645\u0642\u0637\u0639.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u062a\u0642\u0627\u0637\u0639 <code class=\"kbd\">y = 2x \u2212 1<\/code> \u0645\u0639 \u0645\u062d\u0648\u0631 <code class=\"kbd\">y<\/code>.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641 \u0628\u064a\u0646 <code class=\"kbd\">(4,\u22122)<\/code> \u0648 <code class=\"kbd\">(\u22126,8)<\/code>.<\/li>\n <li>\u0627\u062d\u0633\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 <code class=\"kbd\">(2,\u22121)<\/code> \u0648 <code class=\"kbd\">(\u22121,5)<\/code>.<\/li>\n <li>\u0625\u0630\u0627 \u0643\u0627\u0646 \u062e\u0637\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u0627\u0646 \u0648\u0645\u064a\u0644 \u0627\u0644\u0623\u0648\u0644 <code class=\"kbd\">3<\/code>\u060c \u0641\u0645\u0627 \u0645\u064a\u0644 \u0627\u0644\u062b\u0627\u0646\u064a\u061f<\/li>\n <li>\u0623\u0648\u062c\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0627\u0644\u0645\u0627\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <code class=\"kbd\">(\u22122,\u22123)<\/code> \u0648 <code class=\"kbd\">(4,9)<\/code>.<\/li>\n <li>\u0645\u0627 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u062e\u0637 \u0630\u064a \u0627\u0644\u0645\u064a\u0644 <code class=\"kbd\">0<\/code>\u061f<\/li>\n <li>\u062e\u0637 \u0631\u0623\u0633\u064a \u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">x = \u22125<\/code>\u060c \u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u062a\u0647.<\/li>\n <li>\u062d\u0648\u0651\u0644 <code class=\"kbd\">y \u2212 7 = \u22124(x + 1)<\/code> \u0625\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629.<\/li>\n <li>\u0645\u0627 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(0,3)<\/code> \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 <code class=\"kbd\">y = 3<\/code>\u061f<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u064a\u0644\u0647 <code class=\"kbd\">1\/4<\/code> \u0648\u064a\u0642\u0637\u0639 <code class=\"kbd\">y<\/code> \u0639\u0646\u062f <code class=\"kbd\">\u22122<\/code>.<\/li>\n <li>\u062d\u062f\u0651\u062f \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0627\u0637 <code class=\"kbd\">(0,0)<\/code>\u060c <code class=\"kbd\">(2,2)<\/code>\u060c <code class=\"kbd\">(3,3)<\/code> \u0639\u0644\u0649 \u062e\u0637 \u0648\u0627\u062d\u062f.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0637\u0648\u0644 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0648\u0627\u0635\u0644\u0629 \u0628\u064a\u0646 <code class=\"kbd\">(a,b)<\/code> \u0648 <code class=\"kbd\">(a+3,b\u22124)<\/code>.<\/li>\n <li>\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0644\u0625\u062d\u062f\u0627\u062b\u064a\u064a <code class=\"kbd\">x<\/code> \u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u0647\u0648 5\u060c \u0641\u0645\u0627 \u0625\u062d\u062f\u0627\u062b\u064a <code class=\"kbd\">x<\/code> \u0644\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641\u0647\u0645\u0627\u061f<\/li>\n <li>\u062c\u062f \u0645\u064a\u0644 \u062e\u0637 \u064a\u0645\u0631 \u0628\u0646\u0642\u0637\u062a\u064a\u0646 \u0625\u062d\u062f\u0627\u0647\u0645\u0627 <code class=\"kbd\">(\u22121,2)<\/code> \u0648\u0627\u0644\u0623\u062e\u0631\u0649 <code class=\"kbd\">(\u22121,\u22124)<\/code>.<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u0648\u0627\u0632\u064d \u0644\u0640 <code class=\"kbd\">4x \u2212 y + 2 = 0<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(1,1)<\/code>.<\/li>\n <\/ol>\n\n <details>\n <summary>\u0625\u062c\u0627\u0628\u0627\u062a \u0645\u062e\u062a\u0635\u0631\u0629<\/summary>\n <ol>\n <li><code class=\"kbd\">m = (\u22127 \u2212 5)\/(1 \u2212 (\u22123)) = \u221212\/4 = \u22123<\/code>.<\/li>\n <li><code class=\"kbd\">y = \u22123x + 4<\/code>.<\/li>\n <li>\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629: <code class=\"kbd\">2x \u2212 4y + 8=0 \u21d2 y = (1\/2)x + 2<\/code> \u0644\u064a\u0633\u062a \u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u0644\u062b\u0627\u0646\u064a\u0629 (\u0645\u0642\u0627\u0637\u0639 \u0645\u062e\u062a\u0644\u0641\u0629) \u0644\u0643\u0646 \u0627\u0644\u0645\u064a\u0644 \u0646\u0641\u0633\u0647 \u21d2 \u0646\u0639\u0645 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646.<\/li>\n <li>\u0627\u0644\u0645\u064a\u0644 \u0627\u0644\u0639\u0645\u0648\u062f\u064a <code class=\"kbd\">3\/2<\/code> \u0628\u0625\u0634\u0627\u0631\u0629 \u0645\u0648\u062c\u0628\u0629 \u21d2 <code class=\"kbd\">y \u2212 2 = (3\/2)(x + 3)<\/code> \u21d2 <code class=\"kbd\">y = (3\/2)x + 13\/2<\/code>.<\/li>\n <li><code class=\"kbd\">2y = \u22123x + 10 \u21d2 y = (\u22123\/2)x + 5<\/code>.<\/li>\n <li>\u0639\u0646\u062f <code class=\"kbd\">x=0<\/code> \u21d2 <code class=\"kbd\">y = \u22121<\/code> \u21d2 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(0,\u22121)<\/code>.<\/li>\n <li><code class=\"kbd\">M = ((4 + (\u22126))\/2 , (\u22122 + 8)\/2) = (\u22121, 3)<\/code>.<\/li>\n <li><code class=\"kbd\">\u221a[(\u22121 \u2212 2)^2 + (5 \u2212 (\u22121))^2] = \u221a[9 + 36] = \u221a45 \u2248 6.708<\/code>.<\/li>\n <li><code class=\"kbd\">m_2 = \u22121\/3<\/code>.<\/li>\n <li><code class=\"kbd\">m = (9 \u2212 (\u22123))\/(4 \u2212 (\u22122)) = 12\/6 = 2<\/code> \u21d2 <code class=\"kbd\">y \u2212 (\u22123) = 2(x \u2212 (\u22122)) \u21d2 y = 2x + 1<\/code>.<\/li>\n <li>\u0623\u0641\u0642\u064a.<\/li>\n <li><code class=\"kbd\">x = \u22125<\/code>.<\/li>\n <li><code class=\"kbd\">y \u2212 7 = \u22124x \u2212 4 \u21d2 4x + y + (\u22127 + 4) = 0 \u21d2 4x + y \u2212 3 = 0<\/code>.<\/li>\n <li>\u0635\u0641\u0631 (\u0646\u0641\u0633 \u0642\u064a\u0645\u0629 <code class=\"kbd\">y<\/code>).<\/li>\n <li><code class=\"kbd\">y = (1\/4)x \u2212 2<\/code>.<\/li>\n <li>\u0646\u0639\u0645\u060c \u062c\u0645\u064a\u0639\u0647\u0627 \u062a\u062d\u0642\u0642 <code class=\"kbd\">y = x<\/code>.<\/li>\n <li><code class=\"kbd\">\u221a(3^2 + (\u22124)^2) = 5<\/code>.<\/li>\n <li>\u0647\u0648 \u0646\u0641\u0633\u0647 5.<\/li>\n <li>\u063a\u064a\u0631 \u0645\u0639\u0631\u0651\u0641 (\u062e\u0637 \u0631\u0623\u0633\u064a).<\/li>\n <li>\u0646\u0641\u0633 \u0627\u0644\u0645\u064a\u0644: <code class=\"kbd\">y = 4x + b<\/code>. \u0627\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">1 = 4\u00b71 + b \u21d2 b = \u22123<\/code> \u21d2 <code class=\"kbd\">y = 4x \u2212 3<\/code>.<\/li>\n <\/ol>\n <\/details>\n <\/section>\n\n <section id=\"mistakes\">\n <h2>\u26a0\ufe0f \u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629 + \u0646\u0635\u0627\u0626\u062d \u0627\u0644\u0645\u0630\u0627\u0643\u0631\u0629<\/h2>\n <div class=\"grid g2\">\n <div class=\"warn\">\n <strong>\u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629:<\/strong>\n <ul>\n <li>\u0627\u0644\u062e\u0644\u0637 \u0628\u064a\u0646 \u0627\u0644\u0645\u064a\u0644 \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u0631\u0651\u0641 (\u0639\u0645\u0648\u062f\u064a) \u0648\u0627\u0644\u0645\u064a\u0644 \u0635\u0641\u0631 (\u0623\u0641\u0642\u064a).<\/li>\n <li>\u0646\u0633\u064a\u0627\u0646 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0646\u0642\u0627\u0637 \u0641\u064a \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u064a\u0644\u061b \u0627\u0646\u062a\u0628\u0647 \u0644\u0640 <code class=\"kbd\">(y2 \u2212 y1)\/(x2 \u2212 x1)<\/code>.<\/li>\n <li>\u0639\u062f\u0645 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0641\u064a\u062f\u0629 \u0639\u0646\u062f \u0627\u0644\u0631\u0633\u0645.<\/li>\n <\/ul>\n <\/div>\n <div class=\"tips\">\n <strong>\u0631\u0648\u062a\u064a\u0646 30 \u062f\u0642\u064a\u0642\u0629:<\/strong>\n <ol>\n <li>10 \u062f\u0642\u0627\u0626\u0642 \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0635\u064a\u063a.<\/li>\n <li>15 \u062f\u0642\u064a\u0642\u0629 \u0645\u0633\u0627\u0626\u0644 \u0646\u0642\u0637\u062a\u064a\u0646\/\u0646\u0642\u0637\u0629-\u0645\u064a\u0644.<\/li>\n <li>5 \u062f\u0642\u0627\u0626\u0642 \u0628\u0646\u0643 \u0627\u0644\u0623\u062e\u0637\u0627\u0621.<\/li>\n <\/ol>\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"cheatsheet\">\n <h2>\ud83d\udcce \u0645\u0644\u062e\u0635 \u0633\u0631\u064a\u0639 (Cheat Sheet)<\/h2>\n <table>\n <thead><tr><th>\u0627\u0644\u0645\u0641\u0647\u0648\u0645<\/th><th>\u0627\u0644\u0635\u064a\u063a\u0629<\/th><th>\u0645\u0644\u0627\u062d\u0638\u0629<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>\u0627\u0644\u0645\u064a\u0644<\/td><td><code class=\"kbd\">m = (y2 \u2212 y1)\/(x2 \u2212 x1)<\/code><\/td><td>\u062a\u063a\u064a\u0651\u0631 \u0631\u0623\u0633\u064a\/\u0623\u0641\u0642\u064a<\/td><\/tr>\n <tr><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td><code class=\"kbd\">y = mx + b<\/code><\/td><td>\u0633\u0647\u0644 \u0644\u0644\u0631\u0633\u0645<\/td><\/tr>\n <tr><td>\u0646\u0642\u0637\u0629-\u0645\u064a\u0644<\/td><td><code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code><\/td><td>\u0645\u0628\u0627\u0634\u0631 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0645\u064a\u0644<\/td><\/tr>\n <tr><td>\u0639\u0627\u0645\u0651\u0629<\/td><td><code class=\"kbd\">Ax + By + C = 0<\/code><\/td><td>\u0644\u062a\u062d\u0644\u064a\u0644 \u062e\u0648\u0627\u0635 \u0627\u0644\u062e\u0637<\/td><\/tr>\n <tr><td>\u0645\u0646\u062a\u0635\u0641<\/td><td><code class=\"kbd\">M((x1+x2)\/2,(y1+y2)\/2)<\/code><\/td><td>\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u064a\u0646<\/td><\/tr>\n <tr><td>\u0627\u0644\u0645\u0633\u0627\u0641\u0629<\/td><td><code class=\"kbd\">\u221a[(\u0394x)^2 + (\u0394y)^2]<\/code><\/td><td>\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633<\/td><\/tr>\n <tr><td>\u0639\u0645\u0648\u062f\u064a<\/td><td><code class=\"kbd\">m_2 = \u22121\/m_1<\/code><\/td><td>\u0645\u064a\u0644 \u0633\u0627\u0644\u0628 \u0645\u0642\u0644\u0648\u0628<\/td><\/tr>\n <\/tbody>\n <\/table>\n <div class=\"cta\">\n \u0627\u0631\u0628\u0637 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633 \u0628\u062f\u0631\u0648\u0633 <span class=\"tag\">\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062e\u0637\u064a\u0629<\/span> \u0648<span class=\"tag\">\u0627\u0644\u0646\u0645\u0630\u062c\u0629<\/span> \u0644\u062a\u0643\u0648\u064a\u0646 \u0633\u0644\u0633\u0644\u0629 \u0645\u062a\u0643\u0627\u0645\u0644\u0629 \u0644\u0637\u0644\u0627\u0628\u0643.\n <\/div>\n <\/section>\n\n <p class=\"foot\">\u00a9 \u0645\u062d\u062a\u0648\u0649 \u062a\u0639\u0644\u064a\u0645\u064a \u0639\u0627\u0644\u064a \u0627\u0644\u0642\u064a\u0645\u0629 \u2014 \u062c\u0627\u0647\u0632 \u0644\u0644\u0646\u0634\u0631 \u0643\u0640 HTML. \u064a\u0645\u0643\u0646\u0643 \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0644\u0648\u0646 \u0639\u0628\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0651\u0631 <code class=\"kbd\">--brand<\/code>.<\/p>\n<\/article>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 (\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a) \ud83d\udcd0 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 \u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a \u0645\u0631\u062c\u0639 \u0634\u0627\u0645\u0644 \u064a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u0641\u0647\u0645 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u0648\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0634\u0628\u0643\u0629. \u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a \ud83c\udfaf \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0651\u0645 \u0648\u0627\u0644\u0645\u062a\u0637\u0644\u0628\u0627\u062a \ud83d\uddfa\ufe0f […]<\/p>\n","protected":false},"author":1,"featured_media":8892,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[840],"tags":[],"class_list":["post-8891","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computer"],"_links":{"self":[{"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/posts\/8891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/afedne.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8891"}],"version-history":[{"count":1,"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/posts\/8891\/revisions"}],"predecessor-version":[{"id":8893,"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/posts\/8891\/revisions\/8893"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/afedne.info\/index.php?rest_route=\/wp\/v2\/media\/8892"}],"wp:attachment":[{"href":"https:\/\/afedne.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/afedne.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/afedne.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":8891,"date":"2025-08-24T09:00:31","date_gmt":"2025-08-24T06:00:31","guid":{"rendered":"https:\/\/afedne.info\/?p=8891"},"modified":"2025-08-24T09:00:31","modified_gmt":"2025-08-24T06:00:31","slug":"%d8%a7%d9%84%d9%87%d9%86%d8%af%d8%b3%d8%a9-%d8%a7%d9%84%d8%aa%d8%ad%d9%84%d9%8a%d9%84%d9%8a%d8%a9-%d9%84%d9%84%d8%b5%d9%81-%d8%a7%d9%84%d8%b9%d8%a7%d8%b4%d8%b1-%d8%a7%d9%84%d9%85%d9%8a%d9%84%d8%8c","status":"publish","type":"post","link":"https:\/\/afedne.info\/?p=8891","title":{"rendered":"\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 (\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a)"},"content":{"rendered":"\n\n\n\n\n\n\n\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 (\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a)<\/title>\n<style>\n :root{\n --brand:#bdb76b; \/* \u0630\u0647\u0628\u064a \u0641\u0627\u062a\u062d *\/\n --ink:#0f172a;\n --sub:#475569;\n --muted:#64748b;\n --chip:#f8fafc;\n --note:#fffbea;\n --note-b:#fde68a;\n --tips:#f0fdf4;\n --tips-b:#bbf7d0;\n --warn:#fff1f2;\n --warn-b:#fecdd3;\n }\n html,body{background:#ffffff; color:#111; font-family:\"Segoe UI\",Tahoma,Arial,sans-serif; line-height:1.9; margin:0}\n article{max-width:980px; margin:24px auto; padding:24px}\n h1,h2,h3{color:var(--ink); margin:1.2em 0 .5em}\n h1{font-size:32px} h2{font-size:24px} h3{font-size:19px}\n p{margin:.8em 0}\n .sub{color:var(--sub)}\n .pill{display:inline-block; padding:.2em .6em; border-radius:999px; background:var(--brand); color:#111; font-weight:700; font-size:12px; margin-left:6px}\n .toc{background:var(--chip); border:1px solid #e2e8f0; border-radius:14px; padding:14px 16px}\n .toc a{color:#111; text-decoration:none}\n .toc ol{margin:.5em 1.2em}\n .note{background:var(--note); border:1px solid var(--note-b); border-radius:12px; padding:12px 14px}\n .tips{background:var(--tips); border:1px solid var(--tips-b); border-radius:12px; padding:12px 14px}\n .warn{background:var(--warn); border:1px solid var(--warn-b); border-radius:12px; padding:12px 14px}\n .grid{display:grid; gap:12px}\n .g2{grid-template-columns:repeat(2,minmax(0,1fr))}\n .g3{grid-template-columns:repeat(3,minmax(0,1fr))}\n @media(max-width:900px){ .g3{grid-template-columns:1fr} }\n @media(max-width:800px){ .g2{grid-template-columns:1fr} }\n figure{margin:16px auto; text-align:center}\n figcaption{font-size:13px; color:var(--muted)}\n table{border-collapse:collapse; width:100%; margin:14px 0; font-size:15px}\n th,td{border:1px solid #e5e7eb; padding:8px 10px; text-align:right}\n th{background:#f8fafc}\n code.kbd{font-family:ui-monospace,Menlo,monospace; background:#f1f5f9; padding:2px 6px; border-radius:6px}\n .badge{background:#f1f5f9; border:1px dashed var(--brand); border-radius:10px; padding:.3em .6em; font-size:12px; color:#111}\n details{background:#f8fafc; border:1px solid #e2e8f0; padding:10px 12px; border-radius:12px; margin:10px 0}\n summary{cursor:pointer; font-weight:700}\n .cta{background:#eef2ff; border:1px solid #c7d2fe; border-radius:12px; padding:12px 14px}\n .foot{color:var(--muted); font-size:13px; margin-top:28px}\n .tag{background:#e2e8f0; color:#111; border-radius:8px; padding:.1em .5em; font-size:12px; margin-left:6px}\n .hr{height:1px; background:#e2e8f0; margin:18px 0}\n<\/style>\n<\/head>\n<body>\n<article>\n <header>\n <h1>\ud83d\udcd0 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 <span class=\"pill\">\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a<\/span><\/h1>\n <p class=\"sub\">\u0645\u0631\u062c\u0639 \u0634\u0627\u0645\u0644 \u064a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u0641\u0647\u0645 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u0648\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0634\u0628\u0643\u0629.<\/p>\n <\/header>\n\n <section class=\"toc\">\n <strong>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/strong>\n <ol>\n <li><a href=\"#objectives\">\ud83c\udfaf \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0651\u0645 \u0648\u0627\u0644\u0645\u062a\u0637\u0644\u0628\u0627\u062a<\/a><\/li>\n <li><a href=\"#plane\">\ud83d\uddfa\ufe0f \u0645\u0631\u0627\u062c\u0639\u0629 \u0633\u0631\u064a\u0639\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0627\u0644\u0645\u062d\u0627\u0648\u0631<\/a><\/li>\n <li><a href=\"#slope\">\ud83d\udcc8 \u0627\u0644\u0645\u064a\u0644: \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u062a\u0641\u0633\u064a\u0631<\/a><\/li>\n <li><a href=\"#equations\">\u270d\ufe0f \u0635\u064a\u063a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 (\u0645\u064a\u0644-\u0645\u0642\u0637\u0639\u060c \u0646\u0642\u0637\u0629-\u0645\u064a\u0644\u060c \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629)<\/a><\/li>\n <li><a href=\"#parallel\">\u2194\ufe0f \u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0648\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/a><\/li>\n <li><a href=\"#distance-midpoint\">\ud83d\udccf \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629<\/a><\/li>\n <li><a href=\"#models\">\ud83e\udde9 \u0645\u0633\u0627\u0626\u0644 \u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0645\u0646 \u0627\u0644\u0648\u0627\u0642\u0639<\/a><\/li>\n <li><a href=\"#practice\">\ud83d\udcdd 20 \u062a\u0645\u0631\u064a\u0646\u064b\u0627 \u0645\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0645\u062e\u062a\u0635\u0631\u0629<\/a><\/li>\n <li><a href=\"#mistakes\">\u26a0\ufe0f \u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629 + \u0646\u0635\u0627\u0626\u062d \u0627\u0644\u0645\u0630\u0627\u0643\u0631\u0629<\/a><\/li>\n <li><a href=\"#cheatsheet\">\ud83d\udcce \u0645\u0644\u062e\u0635 \u0633\u0631\u064a\u0639 (Cheat Sheet)<\/a><\/li>\n <\/ol>\n <\/section>\n\n <section id=\"objectives\">\n <h2>\ud83c\udfaf \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0651\u0645 \u0648\u0627\u0644\u0645\u062a\u0637\u0644\u0628\u0627\u062a<\/h2>\n <div class=\"grid g2\">\n <div class=\"tips\">\n <strong>\u0633\u062a\u062a\u0639\u0644\u0645 \u0623\u0646:<\/strong>\n <ul>\n <li>\u062a\u062d\u0633\u0628 \u0627\u0644\u0645\u064a\u0644 \u0648\u062a\u0641\u0633\u0631\u0647 \u0643\u0640 <em>\u0645\u0639\u062f\u0644 \u062a\u063a\u064a\u0651\u0631<\/em>.<\/li>\n <li>\u062a\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0633\u062a\u0642\u064a\u0645 \u0628\u0623\u0643\u062b\u0631 \u0645\u0646 \u0635\u064a\u063a\u0629 \u0648\u062a\u062d\u0648\u0651\u0644 \u0628\u064a\u0646\u0647\u0627.<\/li>\n <li>\u062a\u062c\u062f \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641 \u0628\u062f\u0642\u0629.<\/li>\n <li>\u062a\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0632\u064a \u0648\u0627\u0644\u062a\u0639\u0627\u0645\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u064a\u0644.<\/li>\n <\/ul>\n <\/div>\n <div class=\"note\">\n <strong>\u0645\u0631\u0627\u062c\u0639\u0629 \u0644\u0627\u0632\u0645\u0629:<\/strong>\n <ul>\n <li>\u062a\u0631\u062a\u064a\u0628 \u0623\u0632\u0648\u0627\u062c: <code class=\"kbd\">(x,y)<\/code> \u0648\u062a\u062d\u062f\u064a\u062f \u0631\u0628\u0639 \u0627\u0644\u0646\u0642\u0637\u0629.<\/li>\n <li>\u0639\u0645\u0644\u064a\u0627\u062a \u062c\u0628\u0631\u064a\u0629 \u0623\u0633\u0627\u0633\u064a\u0629.<\/li>\n <\/ul>\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"plane\">\n <h2>\ud83d\uddfa\ufe0f \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a<\/h2>\n <p>\u064a\u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u062d\u0648\u0631\u0627\u0646 <code class=\"kbd\">x<\/code> \u0648 <code class=\"kbd\">y<\/code> \u0639\u0646\u062f \u0627\u0644\u0623\u0635\u0644 <code class=\"kbd\">(0,0)<\/code>\u060c \u0648\u062a\u0642\u0633\u0645 \u0627\u0644\u0645\u0633\u062a\u0648\u064a \u0625\u0644\u0649 \u0623\u0631\u0628\u0639\u0629 \u0623\u0631\u0628\u0627\u0639. \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u062a\u062d\u062f\u062f \u0627\u0644\u0631\u0628\u0639.<\/p>\n <div class=\"grid g2\">\n <div>\n <h3>\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0631\u0628\u0639<\/h3>\n <ul>\n <li><strong>\u0627\u0644\u0631\u0628\u0639 \u0627\u0644\u0623\u0648\u0644:<\/strong> <code class=\"kbd\">(+,+)<\/code><\/li>\n <li><strong>\u0627\u0644\u062b\u0627\u0646\u064a:<\/strong> <code class=\"kbd\">(\u2212,+)<\/code><\/li>\n <li><strong>\u0627\u0644\u062b\u0627\u0644\u062b:<\/strong> <code class=\"kbd\">(\u2212,\u2212)<\/code><\/li>\n <li><strong>\u0627\u0644\u0631\u0627\u0628\u0639:<\/strong> <code class=\"kbd\">(+,\u2212)<\/code><\/li>\n <\/ul>\n <\/div>\n <div class=\"tips\">\n <strong>\u0645\u062b\u0627\u0644 \u0633\u0631\u064a\u0639:<\/strong> \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(\u22123,4)<\/code> \u062a\u0642\u0639 \u0641\u064a \u0627\u0644\u0631\u0628\u0639 \u0627\u0644\u062b\u0627\u0646\u064a\u061b \u0644\u0623\u0646\u0647\u0627 \u0633\u0627\u0644\u0628\u0629 \u0639\u0644\u0649 <code class=\"kbd\">x<\/code> \u0648\u0645\u0648\u062c\u0628\u0629 \u0639\u0644\u0649 <code class=\"kbd\">y<\/code>.\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"slope\">\n <h2>\ud83d\udcc8 \u0627\u0644\u0645\u064a\u0644: \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u062a\u0641\u0633\u064a\u0631<\/h2>\n <p><strong>\u0627\u0644\u0645\u064a\u0644<\/strong> \u064a\u0633\u0627\u0648\u064a \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u062a\u063a\u064a\u0651\u0631 \u0627\u0644\u0631\u0623\u0633\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u063a\u064a\u0651\u0631 \u0627\u0644\u0623\u0641\u0642\u064a: <code class=\"kbd\">m = (y2 \u2212 y1) \/ (x2 \u2212 x1)<\/code>. \u064a\u0645\u062b\u0651\u0644 <em>\u0645\u062f\u0649 \u0627\u0631\u062a\u0641\u0627\u0639<\/em> \u0627\u0644\u062e\u0637 \u0644\u0643\u0644 \u062e\u0637\u0648\u0629 \u064a\u0645\u064a\u0646\u064b\u0627.<\/p>\n <div class=\"grid g2\">\n <div>\n <h3>\u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u0645\u064a\u0644<\/h3>\n <ul>\n <li><span class=\"badge\">\u0645\u0648\u062c\u0628<\/span>: \u0627\u0644\u062e\u0637 \u064a\u0635\u0639\u062f \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u0625\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646.<\/li>\n <li><span class=\"badge\">\u0633\u0627\u0644\u0628<\/span>: \u0627\u0644\u062e\u0637 \u064a\u0647\u0628\u0637.<\/li>\n <li><span class=\"badge\">\u0635\u0641\u0631<\/span>: \u062e\u0637 \u0623\u0641\u0642\u064a.<\/li>\n <li><span class=\"badge\">\u063a\u064a\u0631 \u0645\u0639\u0631\u0651\u0641<\/span>: \u062e\u0637 \u0631\u0623\u0633\u064a (\u062a\u0642\u0633\u064a\u0645 \u0639\u0644\u0649 \u0635\u0641\u0631).<\/li>\n <\/ul>\n <\/div>\n <div>\n <h3>\u0645\u062b\u0627\u0644 1 (\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u064a\u0644)<\/h3>\n <p>\u0644\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <code class=\"kbd\">A(\u22122,1)<\/code> \u0648 <code class=\"kbd\">B(4,7)<\/code>:<\/p>\n <p><code class=\"kbd\">m = (7 \u2212 1) \/ (4 \u2212 (\u22122)) = 6 \/ 6 = 1<\/code>.<\/p>\n <\/div>\n <\/div>\n\n <h3>\u0645\u062b\u0627\u0644 2 (\u0645\u064a\u0644 \u0645\u0646 \u062c\u062f\u0648\u0644 \u0642\u064a\u0645)<\/h3>\n <table>\n <thead><tr><th>x<\/th><th>y<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>0<\/td><td>2<\/td><\/tr>\n <tr><td>3<\/td><td>8<\/td><\/tr>\n <\/tbody>\n <\/table>\n <p><code class=\"kbd\">m = (8 \u2212 2) \/ (3 \u2212 0) = 6\/3 = 2<\/code>.<\/p>\n <\/section>\n\n <section id=\"equations\">\n <h2>\u270d\ufe0f \u0635\u064a\u063a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645<\/h2>\n <div class=\"grid g2\">\n <div>\n <h3>1) \u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/h3>\n <p><code class=\"kbd\">y = mx + b<\/code> \u062d\u064a\u062b <span class=\"badge\">m<\/span> \u0627\u0644\u0645\u064a\u0644 \u0648 <span class=\"badge\">b<\/span> \u062a\u0642\u0627\u0637\u0639 <code class=\"kbd\">y<\/code>.<\/p>\n <\/div>\n <div>\n <h3>2) \u0646\u0642\u0637\u0629-\u0645\u064a\u0644<\/h3>\n <p><code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code> \u0645\u0641\u064a\u062f\u0629 \u0639\u0646\u062f \u0645\u0639\u0631\u0641\u0629 \u0646\u0642\u0637\u0629 \u0648\u0627\u0644\u0645\u064a\u0644.<\/p>\n <\/div>\n <\/div>\n <h3>3) \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629<\/h3>\n <p><code class=\"kbd\">Ax + By + C = 0<\/code> \u0645\u0639 <code class=\"kbd\">A,B<\/code> \u0644\u064a\u0633\u0627 \u0643\u0644\u0627\u0647\u0645\u0627 \u0635\u0641\u0631\u064b\u0627. \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u062d\u0648\u064a\u0644 \u0628\u064a\u0646 \u0627\u0644\u0635\u064a\u063a \u0628\u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0648\u0627\u0644\u062c\u0645\u0639.<\/p>\n\n <h3>\u0645\u062b\u0627\u0644 3 (\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0645\u064a\u0644)<\/h3>\n <p>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(2,\u22121)<\/code> \u0648\u0645\u064a\u0644\u0647 <code class=\"kbd\">3<\/code>:<\/p>\n <ol>\n <li><code class=\"kbd\">y \u2212 (\u22121) = 3(x \u2212 2)<\/code> \u21d2 <code class=\"kbd\">y + 1 = 3x \u2212 6<\/code>.<\/li>\n <li><code class=\"kbd\">y = 3x \u2212 7<\/code>.<\/li>\n <\/ol>\n\n <h3>\u0645\u062b\u0627\u0644 4 (\u0645\u0646 \u0646\u0642\u0637\u062a\u064a\u0646)<\/h3>\n <p>\u0627\u0644\u0646\u0642\u0637\u062a\u0627\u0646 <code class=\"kbd\">A(1,4)<\/code> \u0648 <code class=\"kbd\">B(5,\u22122)<\/code>:<\/p>\n <ol>\n <li>\u0627\u0644\u0645\u064a\u0644: <code class=\"kbd\">m = (\u22122 \u2212 4)\/(5 \u2212 1) = \u22126\/4 = \u22123\/2<\/code>.<\/li>\n <li>\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0642\u0637\u0629-\u0645\u064a\u0644 \u0645\u0639 <code class=\"kbd\">A<\/code>: <code class=\"kbd\">y \u2212 4 = (\u22123\/2)(x \u2212 1)<\/code> \u21d2 <code class=\"kbd\">y = (\u22123\/2)x + 3\/2 + 4 = (\u22123\/2)x + 11\/2<\/code>.<\/li>\n <\/ol>\n\n <h3>\u062c\u062f\u0648\u0644 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0633\u0631\u064a\u0639<\/h3>\n <table>\n <thead><tr><th>\u0645\u0646<\/th><th>\u0625\u0644\u0649<\/th><th>\u0627\u0644\u062e\u0637\u0648\u0627\u062a<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>\u0646\u0642\u0637\u0629 + \u0645\u064a\u0644<\/td><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u0627\u0633\u062a\u062e\u062f\u0645 <code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code> \u062b\u0645 \u0628\u0633\u0651\u0637 \u0625\u0644\u0649 <code class=\"kbd\">y = mx + b<\/code>.<\/td><\/tr>\n <tr><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u0639\u0627\u0645\u0651\u0629<\/td><td>\u0627\u0646\u0642\u0644 \u0627\u0644\u062d\u062f\u0648\u062f \u0644\u062c\u0647\u0629 \u0648\u0627\u062d\u062f\u0629 \u062b\u0645 \u0631\u062a\u0651\u0628: <code class=\"kbd\">mx \u2212 y + b = 0<\/code>.<\/td><\/tr>\n <tr><td>\u0639\u0627\u0645\u0651\u0629<\/td><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td>\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0640 <code class=\"kbd\">y<\/code>: <code class=\"kbd\">y = (\u2212A\/B)x \u2212 C\/B<\/code> (\u0625\u0630\u0627 <code class=\"kbd\">B\u22600<\/code>).<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/section>\n\n <section id=\"parallel\">\n <h2>\u2194\ufe0f \u062e\u0637\u0648\u0637 \u0645\u062a\u0648\u0627\u0632\u064a\u0629 \u0648\u0645\u062a\u0639\u0627\u0645\u062f\u0629<\/h2>\n <ul>\n <li><strong>\u0627\u0644\u062a\u0648\u0627\u0632\u064a:<\/strong> \u062e\u0637\u0651\u0627\u0646 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646 \u0644\u0647\u0645\u0627 \u0627\u0644\u0645\u064a\u0644 \u0646\u0641\u0633\u0647 <code class=\"kbd\">m_1 = m_2<\/code> (\u0645\u0639 \u0627\u062e\u062a\u0644\u0627\u0641 <code class=\"kbd\">b<\/code>).<\/li>\n <li><strong>\u0627\u0644\u062a\u0639\u0627\u0645\u062f:<\/strong> \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u064a\u0644\u064a\u0647\u0645\u0627 <code class=\"kbd\">m_1 \u00b7 m_2 = \u22121<\/code> \u21d2 <code class=\"kbd\">m_2 = \u22121\/m_1<\/code> (\u0627\u0644\u0645\u064a\u0644 \u0627\u0644\u0633\u0627\u0644\u0628 \u0627\u0644\u0645\u0642\u0644\u0648\u0628).<\/li>\n <\/ul>\n <h3>\u0645\u062b\u0627\u0644 5 (\u0645\u0648\u0627\u0632\u064d)<\/h3>\n <p>\u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u0648\u0627\u0632\u064d \u0644\u0640 <code class=\"kbd\">y = 2x + 1<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(0,\u22123)<\/code> \u0647\u064a <code class=\"kbd\">y = 2x \u2212 3<\/code>.<\/p>\n <h3>\u0645\u062b\u0627\u0644 6 (\u0639\u0645\u0648\u062f\u064a)<\/h3>\n <p>\u062e\u0637 \u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 <code class=\"kbd\">y = (1\/2)x \u2212 4<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(2,1)<\/code> \u0644\u0647 \u0645\u064a\u0644 <code class=\"kbd\">m = \u22122<\/code> \u21d2 <code class=\"kbd\">y \u2212 1 = \u22122(x \u2212 2)<\/code> \u21d2 <code class=\"kbd\">y = \u22122x + 5<\/code>.<\/p>\n <\/section>\n\n <section id=\"distance-midpoint\">\n <h2>\ud83d\udccf \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0648\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641<\/h2>\n <div class=\"grid g2\">\n <div>\n <h3>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646<\/h3>\n <p><code class=\"kbd\">AB = \u221a[(x2 \u2212 x1)^2 + (y2 \u2212 y1)^2]<\/code> (\u0646\u0627\u062a\u062c\u0629 \u0645\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633).<\/p>\n <h4>\u0645\u062b\u0627\u0644 7<\/h4>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 <code class=\"kbd\">A(\u22121,2)<\/code> \u0648 <code class=\"kbd\">B(3,\u22124)<\/code>:<\/p>\n <p><code class=\"kbd\">AB = \u221a[(3 \u2212 (\u22121))^2 + (\u22124 \u2212 2)^2] = \u221a[4^2 + (\u22126)^2] = \u221a(16+36) = \u221a52 \u2248 7.211<\/code>.<\/p>\n <\/div>\n <div>\n <h3>\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629<\/h3>\n <p><code class=\"kbd\">M = ( (x1 + x2)\/2 , (y1 + y2)\/2 )<\/code>.<\/p>\n <h4>\u0645\u062b\u0627\u0644 8<\/h4>\n <p>\u0645\u0646\u062a\u0635\u0641 <code class=\"kbd\">A(\u22121,2)<\/code> \u0648 <code class=\"kbd\">B(3,\u22124)<\/code> \u0647\u0648 <code class=\"kbd\">M(1, \u22121)<\/code>.<\/p>\n <\/div>\n <\/div>\n\n <h3>\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0639\u0646 \u0645\u0633\u062a\u0642\u064a\u0645 (\u0627\u062e\u062a\u064a\u0627\u0631\u064a \u0645\u062a\u0642\u062f\u0651\u0645)<\/h3>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 <code class=\"kbd\">(x0,y0)<\/code> \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 <code class=\"kbd\">Ax + By + C = 0<\/code> \u0647\u064a <code class=\"kbd\">d = |Ax0 + By0 + C| \/ \u221a(A^2 + B^2)<\/code>.<\/p>\n <\/section>\n\n <section id=\"models\">\n <h2>\ud83e\udde9 \u0645\u0633\u0627\u0626\u0644 \u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0645\u0646 \u0627\u0644\u0648\u0627\u0642\u0639<\/h2>\n <h3>\u0645\u062b\u0627\u0644 9 (\u062a\u0643\u0644\u0641\u0629 \u0648\u062a\u063a\u064a\u0651\u0631 \u062b\u0627\u0628\u062a)<\/h3>\n <p>\u062a\u0643\u0644\u0641\u0629 \u0627\u0634\u062a\u0631\u0627\u0643 \u0625\u0646\u062a\u0631\u0646\u062a: 5 \u062f\u0646\u0627\u0646\u064a\u0631 \u062b\u0627\u0628\u062a\u0629 + 0.8 \u062f\u064a\u0646\u0627\u0631 \u0644\u0643\u0644 \u062c\u064a\u062c\u0627\u0628\u0627\u064a\u062a \u0645\u0633\u062a\u062e\u062f\u0645\u0629. \u0627\u0644\u0646\u0645\u0648\u0630\u062c: <code class=\"kbd\">C(x) = 5 + 0.8x<\/code>. \u0627\u0644\u0645\u064a\u0644 0.8 \u064a\u0639\u0646\u064a \u0632\u064a\u0627\u062f\u0629 0.8 \u062f\u064a\u0646\u0627\u0631 \u0644\u0643\u0644 1 \u062c\u064a\u062c\u0627\u0628\u0627\u064a\u062a.<\/p>\n <h3>\u0645\u062b\u0627\u0644 10 (\u062e\u0631\u064a\u0637\u0629 \u0648\u0645\u0633\u0627\u0641\u0629)<\/h3>\n <p>\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062f\u0631\u0633\u0629 <code class=\"kbd\">S(2,3)<\/code> \u0648\u0627\u0644\u0628\u064a\u062a <code class=\"kbd\">H(\u22124,0)<\/code>. \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 <code class=\"kbd\">\u221a[(\u22126)^2 + (\u22123)^2] = \u221a45 \u2248 6.708<\/code> \u0648\u062d\u062f\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u062e\u0631\u064a\u0637\u0629.<\/p>\n <\/section>\n\n <section id=\"practice\">\n <h2>\ud83d\udcdd 20 \u062a\u0645\u0631\u064a\u0646\u064b\u0627 \u0645\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0645\u062e\u062a\u0635\u0631\u0629<\/h2>\n <ol>\n <li>\u0623\u0648\u062c\u062f \u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0648\u0627\u0635\u0644 \u0628\u064a\u0646 <code class=\"kbd\">(\u22123,5)<\/code> \u0648 <code class=\"kbd\">(1,\u22127)<\/code>.<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0627\u0644\u0645\u0627\u0631 \u0628\u0640 <code class=\"kbd\">(0,4)<\/code> \u0648\u0645\u064a\u0644\u0647 <code class=\"kbd\">\u22123<\/code>.<\/li>\n <li>\u0647\u0644 \u0627\u0644\u062e\u0637 <code class=\"kbd\">2x \u2212 4y + 8 = 0<\/code> \u0645\u0648\u0627\u0632\u064a \u0644\u0640 <code class=\"kbd\">y = (1\/2)x \u2212 1<\/code>\u061f<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 <code class=\"kbd\">y = \u2212(2\/3)x + 1<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(\u22123,2)<\/code>.<\/li>\n <li>\u062d\u0648\u0651\u0644 <code class=\"kbd\">3x + 2y \u2212 10 = 0<\/code> \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u064a\u0644-\u0645\u0642\u0637\u0639.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u062a\u0642\u0627\u0637\u0639 <code class=\"kbd\">y = 2x \u2212 1<\/code> \u0645\u0639 \u0645\u062d\u0648\u0631 <code class=\"kbd\">y<\/code>.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641 \u0628\u064a\u0646 <code class=\"kbd\">(4,\u22122)<\/code> \u0648 <code class=\"kbd\">(\u22126,8)<\/code>.<\/li>\n <li>\u0627\u062d\u0633\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 <code class=\"kbd\">(2,\u22121)<\/code> \u0648 <code class=\"kbd\">(\u22121,5)<\/code>.<\/li>\n <li>\u0625\u0630\u0627 \u0643\u0627\u0646 \u062e\u0637\u0627\u0646 \u0645\u062a\u0639\u0627\u0645\u062f\u0627\u0646 \u0648\u0645\u064a\u0644 \u0627\u0644\u0623\u0648\u0644 <code class=\"kbd\">3<\/code>\u060c \u0641\u0645\u0627 \u0645\u064a\u0644 \u0627\u0644\u062b\u0627\u0646\u064a\u061f<\/li>\n <li>\u0623\u0648\u062c\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0627\u0644\u0645\u0627\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 <code class=\"kbd\">(\u22122,\u22123)<\/code> \u0648 <code class=\"kbd\">(4,9)<\/code>.<\/li>\n <li>\u0645\u0627 \u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u062e\u0637 \u0630\u064a \u0627\u0644\u0645\u064a\u0644 <code class=\"kbd\">0<\/code>\u061f<\/li>\n <li>\u062e\u0637 \u0631\u0623\u0633\u064a \u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">x = \u22125<\/code>\u060c \u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u062a\u0647.<\/li>\n <li>\u062d\u0648\u0651\u0644 <code class=\"kbd\">y \u2212 7 = \u22124(x + 1)<\/code> \u0625\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629.<\/li>\n <li>\u0645\u0627 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(0,3)<\/code> \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 <code class=\"kbd\">y = 3<\/code>\u061f<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u064a\u0644\u0647 <code class=\"kbd\">1\/4<\/code> \u0648\u064a\u0642\u0637\u0639 <code class=\"kbd\">y<\/code> \u0639\u0646\u062f <code class=\"kbd\">\u22122<\/code>.<\/li>\n <li>\u062d\u062f\u0651\u062f \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0627\u0637 <code class=\"kbd\">(0,0)<\/code>\u060c <code class=\"kbd\">(2,2)<\/code>\u060c <code class=\"kbd\">(3,3)<\/code> \u0639\u0644\u0649 \u062e\u0637 \u0648\u0627\u062d\u062f.<\/li>\n <li>\u0623\u0648\u062c\u062f \u0637\u0648\u0644 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0648\u0627\u0635\u0644\u0629 \u0628\u064a\u0646 <code class=\"kbd\">(a,b)<\/code> \u0648 <code class=\"kbd\">(a+3,b\u22124)<\/code>.<\/li>\n <li>\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0644\u0625\u062d\u062f\u0627\u062b\u064a\u064a <code class=\"kbd\">x<\/code> \u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u0647\u0648 5\u060c \u0641\u0645\u0627 \u0625\u062d\u062f\u0627\u062b\u064a <code class=\"kbd\">x<\/code> \u0644\u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641\u0647\u0645\u0627\u061f<\/li>\n <li>\u062c\u062f \u0645\u064a\u0644 \u062e\u0637 \u064a\u0645\u0631 \u0628\u0646\u0642\u0637\u062a\u064a\u0646 \u0625\u062d\u062f\u0627\u0647\u0645\u0627 <code class=\"kbd\">(\u22121,2)<\/code> \u0648\u0627\u0644\u0623\u062e\u0631\u0649 <code class=\"kbd\">(\u22121,\u22124)<\/code>.<\/li>\n <li>\u0627\u0643\u062a\u0628 \u0645\u0639\u0627\u062f\u0644\u0629 \u062e\u0637 \u0645\u0648\u0627\u0632\u064d \u0644\u0640 <code class=\"kbd\">4x \u2212 y + 2 = 0<\/code> \u0648\u064a\u0645\u0631 \u0628\u0640 <code class=\"kbd\">(1,1)<\/code>.<\/li>\n <\/ol>\n\n <details>\n <summary>\u0625\u062c\u0627\u0628\u0627\u062a \u0645\u062e\u062a\u0635\u0631\u0629<\/summary>\n <ol>\n <li><code class=\"kbd\">m = (\u22127 \u2212 5)\/(1 \u2212 (\u22123)) = \u221212\/4 = \u22123<\/code>.<\/li>\n <li><code class=\"kbd\">y = \u22123x + 4<\/code>.<\/li>\n <li>\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629: <code class=\"kbd\">2x \u2212 4y + 8=0 \u21d2 y = (1\/2)x + 2<\/code> \u0644\u064a\u0633\u062a \u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u0644\u062b\u0627\u0646\u064a\u0629 (\u0645\u0642\u0627\u0637\u0639 \u0645\u062e\u062a\u0644\u0641\u0629) \u0644\u0643\u0646 \u0627\u0644\u0645\u064a\u0644 \u0646\u0641\u0633\u0647 \u21d2 \u0646\u0639\u0645 \u0645\u062a\u0648\u0627\u0632\u064a\u0627\u0646.<\/li>\n <li>\u0627\u0644\u0645\u064a\u0644 \u0627\u0644\u0639\u0645\u0648\u062f\u064a <code class=\"kbd\">3\/2<\/code> \u0628\u0625\u0634\u0627\u0631\u0629 \u0645\u0648\u062c\u0628\u0629 \u21d2 <code class=\"kbd\">y \u2212 2 = (3\/2)(x + 3)<\/code> \u21d2 <code class=\"kbd\">y = (3\/2)x + 13\/2<\/code>.<\/li>\n <li><code class=\"kbd\">2y = \u22123x + 10 \u21d2 y = (\u22123\/2)x + 5<\/code>.<\/li>\n <li>\u0639\u0646\u062f <code class=\"kbd\">x=0<\/code> \u21d2 <code class=\"kbd\">y = \u22121<\/code> \u21d2 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">(0,\u22121)<\/code>.<\/li>\n <li><code class=\"kbd\">M = ((4 + (\u22126))\/2 , (\u22122 + 8)\/2) = (\u22121, 3)<\/code>.<\/li>\n <li><code class=\"kbd\">\u221a[(\u22121 \u2212 2)^2 + (5 \u2212 (\u22121))^2] = \u221a[9 + 36] = \u221a45 \u2248 6.708<\/code>.<\/li>\n <li><code class=\"kbd\">m_2 = \u22121\/3<\/code>.<\/li>\n <li><code class=\"kbd\">m = (9 \u2212 (\u22123))\/(4 \u2212 (\u22122)) = 12\/6 = 2<\/code> \u21d2 <code class=\"kbd\">y \u2212 (\u22123) = 2(x \u2212 (\u22122)) \u21d2 y = 2x + 1<\/code>.<\/li>\n <li>\u0623\u0641\u0642\u064a.<\/li>\n <li><code class=\"kbd\">x = \u22125<\/code>.<\/li>\n <li><code class=\"kbd\">y \u2212 7 = \u22124x \u2212 4 \u21d2 4x + y + (\u22127 + 4) = 0 \u21d2 4x + y \u2212 3 = 0<\/code>.<\/li>\n <li>\u0635\u0641\u0631 (\u0646\u0641\u0633 \u0642\u064a\u0645\u0629 <code class=\"kbd\">y<\/code>).<\/li>\n <li><code class=\"kbd\">y = (1\/4)x \u2212 2<\/code>.<\/li>\n <li>\u0646\u0639\u0645\u060c \u062c\u0645\u064a\u0639\u0647\u0627 \u062a\u062d\u0642\u0642 <code class=\"kbd\">y = x<\/code>.<\/li>\n <li><code class=\"kbd\">\u221a(3^2 + (\u22124)^2) = 5<\/code>.<\/li>\n <li>\u0647\u0648 \u0646\u0641\u0633\u0647 5.<\/li>\n <li>\u063a\u064a\u0631 \u0645\u0639\u0631\u0651\u0641 (\u062e\u0637 \u0631\u0623\u0633\u064a).<\/li>\n <li>\u0646\u0641\u0633 \u0627\u0644\u0645\u064a\u0644: <code class=\"kbd\">y = 4x + b<\/code>. \u0627\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0646\u0642\u0637\u0629 <code class=\"kbd\">1 = 4\u00b71 + b \u21d2 b = \u22123<\/code> \u21d2 <code class=\"kbd\">y = 4x \u2212 3<\/code>.<\/li>\n <\/ol>\n <\/details>\n <\/section>\n\n <section id=\"mistakes\">\n <h2>\u26a0\ufe0f \u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629 + \u0646\u0635\u0627\u0626\u062d \u0627\u0644\u0645\u0630\u0627\u0643\u0631\u0629<\/h2>\n <div class=\"grid g2\">\n <div class=\"warn\">\n <strong>\u0623\u062e\u0637\u0627\u0621 \u0634\u0627\u0626\u0639\u0629:<\/strong>\n <ul>\n <li>\u0627\u0644\u062e\u0644\u0637 \u0628\u064a\u0646 \u0627\u0644\u0645\u064a\u0644 \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u0631\u0651\u0641 (\u0639\u0645\u0648\u062f\u064a) \u0648\u0627\u0644\u0645\u064a\u0644 \u0635\u0641\u0631 (\u0623\u0641\u0642\u064a).<\/li>\n <li>\u0646\u0633\u064a\u0627\u0646 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0646\u0642\u0627\u0637 \u0641\u064a \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u064a\u0644\u061b \u0627\u0646\u062a\u0628\u0647 \u0644\u0640 <code class=\"kbd\">(y2 \u2212 y1)\/(x2 \u2212 x1)<\/code>.<\/li>\n <li>\u0639\u062f\u0645 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0641\u064a\u062f\u0629 \u0639\u0646\u062f \u0627\u0644\u0631\u0633\u0645.<\/li>\n <\/ul>\n <\/div>\n <div class=\"tips\">\n <strong>\u0631\u0648\u062a\u064a\u0646 30 \u062f\u0642\u064a\u0642\u0629:<\/strong>\n <ol>\n <li>10 \u062f\u0642\u0627\u0626\u0642 \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0635\u064a\u063a.<\/li>\n <li>15 \u062f\u0642\u064a\u0642\u0629 \u0645\u0633\u0627\u0626\u0644 \u0646\u0642\u0637\u062a\u064a\u0646\/\u0646\u0642\u0637\u0629-\u0645\u064a\u0644.<\/li>\n <li>5 \u062f\u0642\u0627\u0626\u0642 \u0628\u0646\u0643 \u0627\u0644\u0623\u062e\u0637\u0627\u0621.<\/li>\n <\/ol>\n <\/div>\n <\/div>\n <\/section>\n\n <section id=\"cheatsheet\">\n <h2>\ud83d\udcce \u0645\u0644\u062e\u0635 \u0633\u0631\u064a\u0639 (Cheat Sheet)<\/h2>\n <table>\n <thead><tr><th>\u0627\u0644\u0645\u0641\u0647\u0648\u0645<\/th><th>\u0627\u0644\u0635\u064a\u063a\u0629<\/th><th>\u0645\u0644\u0627\u062d\u0638\u0629<\/th><\/tr><\/thead>\n <tbody>\n <tr><td>\u0627\u0644\u0645\u064a\u0644<\/td><td><code class=\"kbd\">m = (y2 \u2212 y1)\/(x2 \u2212 x1)<\/code><\/td><td>\u062a\u063a\u064a\u0651\u0631 \u0631\u0623\u0633\u064a\/\u0623\u0641\u0642\u064a<\/td><\/tr>\n <tr><td>\u0645\u064a\u0644-\u0645\u0642\u0637\u0639<\/td><td><code class=\"kbd\">y = mx + b<\/code><\/td><td>\u0633\u0647\u0644 \u0644\u0644\u0631\u0633\u0645<\/td><\/tr>\n <tr><td>\u0646\u0642\u0637\u0629-\u0645\u064a\u0644<\/td><td><code class=\"kbd\">y \u2212 y1 = m(x \u2212 x1)<\/code><\/td><td>\u0645\u0628\u0627\u0634\u0631 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0645\u064a\u0644<\/td><\/tr>\n <tr><td>\u0639\u0627\u0645\u0651\u0629<\/td><td><code class=\"kbd\">Ax + By + C = 0<\/code><\/td><td>\u0644\u062a\u062d\u0644\u064a\u0644 \u062e\u0648\u0627\u0635 \u0627\u0644\u062e\u0637<\/td><\/tr>\n <tr><td>\u0645\u0646\u062a\u0635\u0641<\/td><td><code class=\"kbd\">M((x1+x2)\/2,(y1+y2)\/2)<\/code><\/td><td>\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u064a\u0646<\/td><\/tr>\n <tr><td>\u0627\u0644\u0645\u0633\u0627\u0641\u0629<\/td><td><code class=\"kbd\">\u221a[(\u0394x)^2 + (\u0394y)^2]<\/code><\/td><td>\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633<\/td><\/tr>\n <tr><td>\u0639\u0645\u0648\u062f\u064a<\/td><td><code class=\"kbd\">m_2 = \u22121\/m_1<\/code><\/td><td>\u0645\u064a\u0644 \u0633\u0627\u0644\u0628 \u0645\u0642\u0644\u0648\u0628<\/td><\/tr>\n <\/tbody>\n <\/table>\n <div class=\"cta\">\n \u0627\u0631\u0628\u0637 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633 \u0628\u062f\u0631\u0648\u0633 <span class=\"tag\">\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062e\u0637\u064a\u0629<\/span> \u0648<span class=\"tag\">\u0627\u0644\u0646\u0645\u0630\u062c\u0629<\/span> \u0644\u062a\u0643\u0648\u064a\u0646 \u0633\u0644\u0633\u0644\u0629 \u0645\u062a\u0643\u0627\u0645\u0644\u0629 \u0644\u0637\u0644\u0627\u0628\u0643.\n <\/div>\n <\/section>\n\n <p class=\"foot\">\u00a9 \u0645\u062d\u062a\u0648\u0649 \u062a\u0639\u0644\u064a\u0645\u064a \u0639\u0627\u0644\u064a \u0627\u0644\u0642\u064a\u0645\u0629 \u2014 \u062c\u0627\u0647\u0632 \u0644\u0644\u0646\u0634\u0631 \u0643\u0640 HTML. \u064a\u0645\u0643\u0646\u0643 \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0644\u0648\u0646 \u0639\u0628\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0651\u0631 <code class=\"kbd\">--brand<\/code>.<\/p>\n<\/article>\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 (\u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a) \ud83d\udcd0 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0644\u0644\u0635\u0641 \u0627\u0644\u0639\u0627\u0634\u0631: \u0627\u0644\u0645\u064a\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629 \u0634\u0631\u062d + \u0623\u0645\u062b\u0644\u0629 + \u062a\u062f\u0631\u064a\u0628\u0627\u062a \u0645\u0631\u062c\u0639 \u0634\u0627\u0645\u0644 \u064a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u0641\u0647\u0645 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645\u0629 \u0648\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 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