{"id":225,"date":"2023-07-10T23:13:43","date_gmt":"2023-07-10T23:13:43","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e6%96%9c%e7%8e%87%e5%85%ac%e5%bc%8f\/"},"modified":"2023-07-10T23:13:43","modified_gmt":"2023-07-10T23:13:43","slug":"%e7%9b%b4%e7%ba%bf%e6%96%9c%e7%8e%87%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%9b%b4%e7%ba%bf%e6%96%9c%e7%8e%87%e5%85%ac%e5%bc%8f\/","title":{"rendered":"\u76f4\u7ebf\u7684\u659c\u7387\uff08\u516c\u5f0f\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u76f4\u7ebf\u659c\u7387\u6700\u8be6\u7ec6\u7684\u89e3\u91ca\uff1a\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\u3001\u8ba1\u7b97\u793a\u4f8b\u3001\u76f4\u7ebf\u659c\u7387\u7684\u6982\u5ff5\u610f\u5473\u7740\u4ec0\u4e48\u2026\u2026\u60a8\u8fd8\u5c06\u80fd\u591f\u770b\u5230\u5982\u4f55\u8f7b\u677e\u8bc6\u522b\u659c\u7387\u4ece\u65b9\u7a0b\u4e2d\u753b\u51fa\u4e00\u6761\u76f4\u7ebf\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-pendiente-de-una-recta\"><\/span>\u76f4\u7ebf\u659c\u7387\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"><strong>\u76f4\u7ebf\u7684\u659c\u7387<\/strong>\u7b49\u4e8e\u4e24\u70b9\u4e4b\u95f4\u7684\u5782\u76f4\u4f4d\u79fb\u9664\u4ee5\u8fd9\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u6c34\u5e73\u4f4d\u79fb\u3002<\/p>\n<p style=\"text-align:left\">\u4e5f\u5c31\u662f\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u6761\u7ebf\u4e0a\u7684\u4e24\u4e2a\u70b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64af51bbaed8952d251997515c64b85c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1) \\qquad P_2(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u76f4\u7ebf\u659c\u7387\u7684\u516c\u5f0f\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ca826248e812d4f19056960777cb00f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\Delta y}{\\Delta x} = \\cfrac{y_2-y_1}{x_2-x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"150\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/pente-dune-ligne-1.webp\" alt=\"\u76f4\u7ebf\u7684\u659c\u7387\u662f\u591a\u5c11\" class=\"wp-image-1523\" width=\"328\" height=\"312\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-pendiente-de-una-recta-a-partir-de-dos-puntos\"><\/span>\u8ba1\u7b97\u4e24\u70b9\u76f4\u7ebf\u659c\u7387\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e00\u4e2a\u5982\u4f55\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u76f4\u7ebf\u659c\u7387\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97\u7ecf\u8fc7\u4ee5\u4e0b\u4e24\u70b9\u7684\u76f4\u7ebf\u7684\u659c\u7387\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5625033af5d12379bbc5e375fd06888d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(3,1) \\qquad P_2(5,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u627e\u5230\u8fd9\u6761\u7ebf\u7684\u659c\u7387\uff0c\u53ea\u9700\u5e94\u7528\u5176\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a5b9ed9145447559a6eb62e27c584432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\Delta y}{\\Delta x} = \\cfrac{y_2-y_1}{x_2-x_1}=\\cfrac{7-1}{5-3}=\\cfrac{6}{2} = \\bm{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"281\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u7ebf\u7684\u659c\u7387\u7b49\u4e8e 3\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-la-pendiente-de-una-recta-a-partir-de-su-ecuacion\"><\/span>\u4ece\u65b9\u7a0b\u6c42\u51fa\u76f4\u7ebf\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u5728\u4e0a\u9762\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u521a\u521a\u4e86\u89e3\u4e86\u5982\u4f55\u4ee5\u6570\u503c\u65b9\u5f0f\u786e\u5b9a\u76f4\u7ebf\u7684\u659c\u7387\u3002\u7136\u800c\uff0c\u5e76\u4e0d\u603b\u662f\u9700\u8981\u8fdb\u884c\u8ba1\u7b97\uff0c\u4e5f\u53ef\u4ee5\u4ece\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u786e\u5b9a\u5176\u503c\u3002\u6bcf\u79cd\u7c7b\u578b\u7684\u65b9\u7a0b\u90fd\u4e0d\u540c\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5206\u522b\u5206\u6790\u6bcf\u79cd\u60c5\u51b5\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-explicita-de-la-recta\"><\/span>\u7ed9\u5b9a\u76f4\u7ebf\u7684\u663e\u5f0f\u65b9\u7a0b\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8be5\u76f4\u7ebf\u7684\u663e\u5f0f\u65b9\u7a0b\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f20f0b48ca24d4d8e36d110a7a9fab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\color{blue}\\bm{m}\\color{black}x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"163\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7136\u540e\u662f\u53c2\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5bf9\u5e94\u4e8e\u7ebf\u7684\u659c\u7387\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-punto-pendiente-de-la-recta\"><\/span>\u7ed9\u5b9a\u76f4\u7ebf\u7684\u70b9\u659c\u7387\u65b9\u7a0b\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u76f4\u7ebf\u7684\u70b9\u659c\u7387\u65b9\u7a0b\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-470b8b3f0e00bf809f6089864fe6dd44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -y_0=\\color{blue}\\bm{m}\\color{black}(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5bf9\u5e94\u4e8e\u7ebf\u7684\u659c\u7387\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dada-la-ecuacion-implicita-de-la-recta\"><\/span>\u7ed9\u5b9a\u76f4\u7ebf\u9690\u5f0f\u65b9\u7a0b\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7ed9\u5b9a\u76f4\u7ebf\u7684\u9690\u5f0f\u65b9\u7a0b\uff08\u4e5f\u79f0\u4e3a\u4e00\u822c\u65b9\u7a0b\u6216\u7b1b\u5361\u5c14\u65b9\u7a0b\uff09\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02f4d03229cc8bd79a81b676a8132f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u53ef\u4ee5\u901a\u8fc7\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\u627e\u5230\u8be5\u7ebf\u7684\u659c\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94f59cc7d3c1b4ece0a70a3587fa0a77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-\\cfrac{A}{B}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dado-el-vector-director-de-la-recta\"><\/span>\u8003\u8651\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u662f\u6807\u8bb0\u5176\u65b9\u5411\u7684\u5411\u91cf\u3002\u56e0\u6b64\uff0c\u5982\u679c\u4e00\u6761\u7ebf\u7684\u65b9\u5411\u5411\u91cf\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-867fb10d1409b3d95ff447f6a095219d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6761\u7ebf\u7684\u659c\u7387\u662f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbe7689423f29f352d6a3def8b92e945_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=\\cfrac{\\text{v}_2}{\\text{v}_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"59\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pendiente-dado-un-angulo\"><\/span>\u7ed9\u5b9a\u89d2\u5ea6\u7684\u659c\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6700\u540e\uff0c\u5982\u679c\u4e00\u6761\u7ebf\u5f62\u6210\u4e00\u4e2a\u89d2\u5ea6<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5728\u6a2a\u5750\u6807\u8f74\uff08X\u8f74\uff09\u7684\u6b63\u503c\u90e8\u5206\uff0c\u5176\u659c\u7387\u7b49\u4e8e\u89d2\u5ea6\u7684\u6b63\u5207\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2b29dd45ad9f0c0537a0cf6233ce929_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}(\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"significado-de-la-pendiente-de-una-recta\"><\/span>\u76f4\u7ebf\u659c\u7387\u7684\u542b\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u4e86\u4e0a\u8ff0\u6240\u6709\u4fe1\u606f\uff0c\u6211\u4eec\u5df2\u7ecf\u975e\u5e38\u6e05\u695a\u5982\u4f55\u627e\u5230\u76f4\u7ebf\u7684\u659c\u7387\u3002\u4f46\u5b9e\u9645\u4e0a\u2026\u2026\u76f4\u7ebf\u7684\u659c\u7387\u662f\u4ec0\u4e48\u610f\u601d\uff1f<\/p>\n<p><strong>\u76f4\u7ebf\u7684\u659c\u7387\u8868\u793a\u8be5\u76f4\u7ebf\u76f8\u5bf9\u4e8e\u56fe\u5f62\u7684\u6bcf\u4e2a\u6c34\u5e73\u5355\u4f4d\u4e0a\u5347\u7684\u5782\u76f4\u5355\u4f4d\u3002<\/strong><\/p>\n<p>\u4f8b\u5982\uff0c\u5728\u4e0b\u9762\u7684\u7ebf\u7684\u8868\u793a\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u6bcf\u4e2a\u6c34\u5e73\u5355\u4f4d\u524d\u8fdb 2 \u4e2a\u5782\u76f4\u5355\u4f4d\uff0c\u56e0\u4e3a\u5b83\u7684\u659c\u7387\u7b49\u4e8e 2\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-explicite-d-une-ligne.webp\" alt=\"\u76f4\u7ebf\u7684\u659c\u7387\u662f\u591a\u5c11\" class=\"wp-image-1455\" width=\"341\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b64\u5916\uff0c\u76f4\u7ebf\u7684\u659c\u7387\u4e5f\u8868\u793a\u5176\u9661\u5ced\u7a0b\u5ea6\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u4e00\u6761\u7ebf\u6b63\u5728\u589e\u52a0\uff08\u4e0a\u5347\uff09\uff0c\u5219\u5176\u659c\u7387\u4e3a\u6b63\u3002<\/li>\n<li>\u5982\u679c\u4e00\u6761\u7ebf\u5448\u9012\u51cf\uff08\u4e0b\u964d\uff09\u8d8b\u52bf\uff0c\u5219\u5176\u659c\u7387\u4e3a\u8d1f\u3002<\/li>\n<li>\u5982\u679c\u4e00\u6761\u7ebf\u5b8c\u5168\u6c34\u5e73\uff0c\u5219\u5176\u659c\u7387\u7b49\u4e8e 0\u3002<\/li>\n<li>\u5982\u679c\u4e00\u6761\u7ebf\u5b8c\u5168\u5782\u76f4\uff0c\u5219\u5176\u659c\u7387\u7b49\u4e8e\u65e0\u7a77\u5927\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-167\">\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/pente-positive-ou-negative-de-la-droite.webp\" alt=\"\u6b63\u7ebf\u6216\u8d1f\u7ebf\u7684\u659c\u7387\" class=\"wp-image-1540\" width=\"470\" height=\"238\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/pente-dune-ligne-zero-ou-infinie.webp\" alt=\"\u96f6\u7ebf\u6216\u65e0\u9650\u7ebf\u7684\u659c\u7387\" class=\"wp-image-1541\" width=\"478\" height=\"238\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"posicion-relativa-de-las-rectas\"><\/span>\u7ebf\u7684\u76f8\u5bf9\u4f4d\u7f6e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u4e5f\u53ef\u4ee5\u4ece\u659c\u7387\u7684\u6027\u8d28\u5f97\u77e5\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u4e24\u6761\u7ebf\u6709\u4e0d\u540c\u7684\u659c\u7387\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u4eec<strong>\u76f8\u4ea4<\/strong>\uff0c\u5373\u5b83\u4eec\u76f8\u4ea4\u4e8e\u4e00\u70b9\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/secantes-pente-d-une-ligne.webp\" alt=\"\u76f8\u4ea4\u7ebf \u4e0d\u540c\u7684\u5761\u5ea6\" class=\"wp-image-1549\" width=\"222\" height=\"232\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b64\u5916\uff0c\u4e24\u6761\u7ebf\u4e0e\u659c\u7ebf\u4e4b\u95f4\u7684\u89d2\u5ea6\u53ef\u4ee5\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-95b6b3d8558ce7ad38e9652a3f9f612d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tg}(\\alpha) = \\cfrac{m_2-m_1}{1+m_1\\cdot m_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"157\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5176\u6b21\uff0c\u5982\u679c\u4e24\u6761\u7ebf\u5177\u6709\u76f8\u540c\u7684\u659c\u7387\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u662f<strong>\u5e73\u884c\u7684<\/strong>\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-paralleles-pente-dune-ligne.webp\" alt=\"\u5e73\u884c\u7ebf\u7b49\u659c\u7387\" class=\"wp-image-1550\" width=\"207\" height=\"208\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<ul>\n<li>\u6700\u540e\uff0c\u4e24\u6761<strong>\u5782\u76f4<\/strong>\u6216<strong>\u6b63\u4ea4<\/strong>\u7ebf\uff08\u5f62\u6210 90\u00b0\uff09\u7684\u659c\u7387\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-perpendiculaires-pente-d-une-ligne.webp\" alt=\"\u4e0e\u659c\u7387\u76f8\u5bf9\u7684\u5782\u76f4\u7ebf\" class=\"wp-image-1551\" width=\"183\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8fd9\u662f\u786e\u5b9a\u4e24\u6761\u7ebf\u662f\u5426\u76f8\u4e92\u5e73\u884c\u6216\u5782\u76f4\u7684\u4e00\u79cd\u65b9\u6cd5\uff0c\u4f46\u662f\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\uff0c\u6709\u4e9b\u751a\u81f3\u66f4\u5feb\u3002\u8981\u4e86\u89e3\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u8f6c\u5230<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u884c\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50\/\">\u7ebf\u4e4b\u95f4\u7684<\/a><a href=\"https:\/\/mathority.org\/cn\/\u5782\u76f4\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50-\u5782\u76f4\u5ea6\/\">\u5782\u76f4\u5ea6<\/a>\u548c\u5e73\u884c\u5ea6\u7684\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u8fd9\u4e9b\u9875\u9762\u8fd8\u89e3\u91ca\u4e86\u5982\u4f55\u627e\u5230\u4e0e\u53e6\u4e00\u6761\u5782\u76f4\uff08\u6216\u5e73\u884c\uff09\u7684\u7ebf\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-pendiente-de-una-recta\"><\/span>\u89e3\u51b3\u4e86\u76f4\u7ebf\u7684\u659c\u7387\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6c42\u901a\u8fc7\u4ee5\u4e0b\u4e24\u70b9\u7684\u76f4\u7ebf\u7684\u659c\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1737beb6850f4de1ea0c016cc1bc6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(5,6) \\qquad P_2(8,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u76f4\u7ebf\u7684\u659c\u7387\uff0c\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-704148ba7570ada0ae582712ab7f93e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\Delta y}{\\Delta x} = \\cfrac{y_2-y_1}{x_2-x_1}=\\cfrac{3-6}{8-5}=\\cfrac{-3}{3} = \\bm{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"316\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u8ba1\u7b97\u7ecf\u8fc7\u4ee5\u4e0b\u4e24\u70b9\u7684\u76f4\u7ebf\u7684\u659c\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-092707a43b0264500e478afcfe29aaea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(-3,1) \\qquad P_2(-2,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230\u76f4\u7ebf\u7684\u659c\u7387\uff0c\u60a8\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96bd25846027e66360f0f5125603d20f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\Delta y}{\\Delta x} = \\cfrac{y_2-y_1}{x_2-x_1}=\\cfrac{-4-1}{-2-(-3)}=\\cfrac{-5}{-2+3}=\\cfrac{-5}{1} = \\bm{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"436\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u6bcf\u6761\u7ebf\u7684\u659c\u7387\u662f\u591a\u5c11\uff1f <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d405c8176957af59906c98149714570_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lll} A) \\ y= 2x+3 &amp; \\qquad &amp; B) \\  y-3=4(x+1) \\\\[2ex] C) \\  6x+2y-7=0 &amp; \\qquad &amp; D) \\ \\begin{cases}x=3-t \\\\[2ex] y=1+2t \\end{cases} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"370\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>A)<\/strong>\u8be5\u76f4\u7ebf\u8868\u793a\u4e3a\u9690\u5f0f\u65b9\u7a0b\uff0c\u56e0\u6b64<strong>\u5176\u659c\u7387\u4e3a 2<\/strong> \uff08\u4f34\u968f\u8be5\u65b9\u7a0b\u7684\u9879\uff09<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \uff09\u3002<\/p>\n<p class=\"has-text-align-left\"> <strong>B)<\/strong>\u8be5\u7ebf\u7531\u5176\u70b9\u659c\u7387\u65b9\u7a0b\u5b9a\u4e49\uff0c\u56e0\u6b64<strong>\u5176\u659c\u7387\u4e3a 4<\/strong> \uff08\u62ec\u53f7\u524d\u7684\u6570\u5b57\uff09\u3002<\/p>\n<p class=\"has-text-align-left\"> <strong>C)<\/strong>\u8be5\u76f4\u7ebf\u4e3a\u9690\u5f0f\u65b9\u7a0b\u5f62\u5f0f\uff0c\u56e0\u6b64\u5176\u659c\u7387\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0dd97ea88f88443fc8c46bde067053eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m= - \\cfrac{A}{B} = -\\cfrac{6}{2} = \\bm{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"164\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>D)<\/strong>\u76f4\u7ebf\u662f\u4ee5\u53c2\u6570\u65b9\u7a0b\u7684\u5f62\u5f0f\u5b9a\u4e49\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9996\u5148\u5fc5\u987b\u627e\u5230\u5b83\u7684\u65b9\u5411\u5411\u91cf\uff0c\u7136\u540e\u7528\u5b83\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u76f4\u7ebf\u7684\u659c\u7387\u3002\u56e0\u6b64\uff0c\u65b9\u5411\u5411\u91cf\u7684\u5206\u91cf\u662f\u4f34\u968f\u7cfb\u6570\u7684\u9879<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-920bbf7e23f9c991e14e800ec8003b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u76f4\u7ebf\u7684\u65b9\u5411\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u786e\u5b9a\u76f4\u7ebf\u7684\u659c\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-62e1424e65bcd14a34c4b366789f7b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\cfrac{\\text{v}_2}{\\text{v}_1} = \\cfrac{2}{-1} = \\bm{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"152\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u786e\u5b9a\u6bcf\u6761\u56fe\u5f62\u7ebf\u7684\u659c\u7387\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-dequation-de-la-ligne-explicite.webp\" alt=\"\u9010\u6b65\u6c42\u89e3\u76f4\u7ebf\u7ec3\u4e60\u7684\u663e\u5f0f\u65b9\u7a0b\" class=\"wp-image-1500\" width=\"377\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"><strong>\u84dd\u8272\u53f3<\/strong><\/p>\n<p class=\"has-text-align-left\">\u84dd\u7ebf\u6bcf X \u589e\u52a0 1 \u4e2a Y\uff0c\u56e0\u6b64<strong>\u5176\u659c\u7387\u7b49\u4e8e 1\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d94dded0dc9c883f82d566d62e2d4b42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u53f3\u7eff\u8272<\/strong><\/p>\n<p class=\"has-text-align-left\">\u7eff\u7ebf\u6bcf X \u589e\u52a0 3 \u4e2a Y\uff0c\u56e0\u6b64<strong>\u5176\u659c\u7387\u4e3a 3<\/strong> \u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-260107cba86a7b21e919180b1130050e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"><strong>\u7ea2\u7ebf<\/strong><\/p>\n<p class=\"has-text-align-left\">\u6bcf\u589e\u52a0\u4e00\u4e2a X\uff0c\u7ea2\u7ebf\u5c31\u4f1a\u51cf\u5c11 2 \u4e2a Y\uff0c\u56e0\u6b64<strong>\u5b83\u7684\u659c\u7387\u7b49\u4e8e -2<\/strong> \u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cb69f8df8ea8c5935576ece37a640c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end 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