{"id":224,"date":"2023-07-10T23:45:14","date_gmt":"2023-07-10T23:45:14","guid":{"rendered":"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/"},"modified":"2023-07-10T23:45:14","modified_gmt":"2023-07-10T23:45:14","slug":"equacao-explicita-de-uma-reta","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/","title":{"rendered":"Equa\u00e7\u00e3o expl\u00edcita da reta"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a equa\u00e7\u00e3o expl\u00edcita de uma reta: o que \u00e9, qual a sua f\u00f3rmula, exemplos de c\u00e1lculo, etc. Voc\u00ea tamb\u00e9m encontrar\u00e1 uma explica\u00e7\u00e3o detalhada do que significa inclina\u00e7\u00e3o e a intercepta\u00e7\u00e3o da equa\u00e7\u00e3o expl\u00edcita. E, al\u00e9m disso, voc\u00ea ver\u00e1 diversos exemplos e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. <\/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=\"%c2%bfque-es-la-ecuacion-explicita-de-la-recta\"><\/span> Qual \u00e9 a equa\u00e7\u00e3o expl\u00edcita da reta?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Lembre-se de que a defini\u00e7\u00e3o matem\u00e1tica de uma reta \u00e9 um conjunto de pontos consecutivos representados na mesma dire\u00e7\u00e3o, sem curvas ou \u00e2ngulos. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Portanto, a <strong>equa\u00e7\u00e3o expl\u00edcita da reta<\/strong> \u00e9 uma forma de expressar matematicamente qualquer reta. Para fazer isso, basta saber a <a href=\"https:\/\/mathority.org\/pt\/formula-de-inclinacao-da-linha\/\">inclina\u00e7\u00e3o da reta<\/a> e o ponto onde ela cruza o eixo Y. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-explicita-de-la-recta\"><\/span> F\u00f3rmula para a equa\u00e7\u00e3o expl\u00edcita da reta <span class=\"ez-toc-section-end\"><\/span><\/h2>\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\"> A f\u00f3rmula para a <strong>equa\u00e7\u00e3o expl\u00edcita da reta<\/strong> \u00e9:<\/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-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;\"> Ouro<\/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> \u00e9 a inclina\u00e7\u00e3o da linha e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> sua intercepta\u00e7\u00e3o em y, ou seja, a altura em que intercepta o eixo Y. <\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Vamos ver <strong>como a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9 calculada<\/strong> atrav\u00e9s de um exemplo:<\/p>\n<ul>\n<li> Escreva a equa\u00e7\u00e3o expl\u00edcita da reta que passa pelo ponto\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b605acb6ff6be36fc4748cc7b06fb3e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> e inclina\u00e7\u00e3o m=2.<\/li>\n<\/ul>\n<p> A f\u00f3rmula para a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9:<\/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-c8bbb40f6658cea3b5ba541c3fbde45f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Neste caso, a afirma\u00e7\u00e3o nos diz que a inclina\u00e7\u00e3o da reta \u00e9 m=2, ent\u00e3o a equa\u00e7\u00e3o da reta ser\u00e1 a seguinte:<\/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-dd5f612b3ddcadb2e740617920ed526c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= 2x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u00c9, portanto, suficiente calcular o coeficiente n. Para fazer isso, devemos substituir um ponto que pertence \u00e0 reta em sua equa\u00e7\u00e3o. E neste caso, a afirma\u00e7\u00e3o nos diz que a reta passa pelo ponto<\/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-9dcf15d7b3e8ffc347543d7d48b719ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,1),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\"><\/p>\n<p> Ainda:<\/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-b605acb6ff6be36fc4748cc7b06fb3e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/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-6d9ded3bdd1109db8afb7ed437954852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= 2x+n \\ \\xrightarrow{x=3 \\ ; \\ y=1} \\ 1=2\\cdot 3 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"278\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> E resolvemos a equa\u00e7\u00e3o resultante para encontrar o valor de n: <\/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-32c011de851560327d8bafd4d00830ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=2\\cdot 3 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -2px;\"><\/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-d85f0212b32499b9140f0e9b9cc2430b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=6 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\"><\/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-0355a5088e699a32086a4c7712400bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-6=n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-4c1601e3ff288c7a2fbb944a90fd1f50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-5 = n\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A equa\u00e7\u00e3o expl\u00edcita da reta \u00e9, portanto:<\/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-9a6e31bb34bf14e75607b88a0b3bcfc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y= 2x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Tenha em mente que al\u00e9m da equa\u00e7\u00e3o expl\u00edcita, existem outras maneiras de expressar analiticamente uma reta. Por exemplo, a <a href=\"https:\/\/mathority.org\/pt\">equa\u00e7\u00e3o vetorial<\/a> , que \u00e9 um tipo de equa\u00e7\u00e3o de reta diferente de todas as outras porque o vetor de dire\u00e7\u00e3o e um ponto da reta s\u00e3o expressos com suas pr\u00f3prias coordenadas. No link voc\u00ea confere o que \u00e9 e porque \u00e9 t\u00e3o especial. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"significado-de-los-parametros-m-y-n\"><\/span> Significado dos par\u00e2metros m e n <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Como vimos na defini\u00e7\u00e3o da equa\u00e7\u00e3o expl\u00edcita da reta, o par\u00e2metro<\/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> \u00e9 a inclina\u00e7\u00e3o da linha e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> sua intercepta\u00e7\u00e3o em y. Mas o que isso significa? Vamos ver isso a partir da representa\u00e7\u00e3o gr\u00e1fica de uma linha: <\/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=\"Qual \u00e9 a equa\u00e7\u00e3o expl\u00edcita da reta y=mx+b\" class=\"wp-image-1455\" width=\"339\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> O termo independente<\/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-565fee0d356edf7fb1f49b6e7eec8e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> <strong>\u00e9 o ponto de intersec\u00e7\u00e3o da linha com o eixo do computador<\/strong> (eixo OY). No gr\u00e1fico acima<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 igual a 1 porque a linha cruza o eixo y em y=1.<\/p>\n<p> Por outro lado, o termo<\/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-f26b1f086c6ad942d7c0dac86a8338fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{m}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> <strong>indica a inclina\u00e7\u00e3o da linha<\/strong> , ou seja, sua inclina\u00e7\u00e3o. Como voc\u00ea pode ver no gr\u00e1fico,<\/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> \u00e9 igual a 2, pois a linha aumenta 2 unidades verticais para 1 unidade horizontal.<\/p>\n<p> Obviamente, se a inclina\u00e7\u00e3o for positiva a fun\u00e7\u00e3o est\u00e1 aumentando (subindo), por outro lado se a inclina\u00e7\u00e3o for negativa a fun\u00e7\u00e3o est\u00e1 diminuindo (descendo).<\/p>\n<h4 class=\"wp-block-heading\"> Calcular a inclina\u00e7\u00e3o de uma linha<\/h4>\n<p> Al\u00e9m disso, existem 3 maneiras diferentes de determinar numericamente a inclina\u00e7\u00e3o de uma linha:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">Dados dois pontos diferentes na linha\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99906702500e51b12e2859cc804a7b57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(x_1,y_1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-460a66d684215738da922dc45a35aed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2(x_2,y_2),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<p> A inclina\u00e7\u00e3o da linha \u00e9 igual a:<\/li>\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<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">Sim\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><\/span> \u00e9 o vetor de dire\u00e7\u00e3o da reta, sua inclina\u00e7\u00e3o \u00e9:<\/li>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60d899a76c2b7588e60dc3734a47019f_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<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">Sim\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><\/span> \u00e9 o \u00e2ngulo formado pela reta com o eixo das abcissas (eixo X), a inclina\u00e7\u00e3o da reta \u00e9 equivalente \u00e0 tangente desse \u00e2ngulo: <\/li>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c76cc82b1d172b2b5af3b053752befac_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<\/ol>\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\/formule-de-l-equation-explicite-d-une-ligne.webp\" alt=\"f\u00f3rmula para a equa\u00e7\u00e3o expl\u00edcita da reta\" class=\"wp-image-1465\" width=\"288\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\"> Posi\u00e7\u00e3o relativa das linhas<\/h4>\n<p> Finalmente, a inclina\u00e7\u00e3o de uma linha tamb\u00e9m \u00e9 usada para conhecer a rela\u00e7\u00e3o entre v\u00e1rias linhas. Como duas retas <strong>paralelas<\/strong> t\u00eam a mesma inclina\u00e7\u00e3o e, por outro lado, se a inclina\u00e7\u00e3o de uma reta \u00e9 o inverso negativo da inclina\u00e7\u00e3o de outra reta, isso significa que essas duas retas s\u00e3o <strong>perpendiculares<\/strong> . <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-173\">\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\/lignes-paralleles-pente-dune-ligne.webp\" alt=\"linhas paralelas com a mesma inclina\u00e7\u00e3o\" class=\"wp-image-1550\" width=\"200\" height=\"201\" 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\/lignes-perpendiculaires-pente-d-une-ligne.webp\" alt=\"\" class=\"wp-image-1551\" width=\"176\" height=\"260\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-la-ecuacion-explicita-de-la-recta-que-pasa-por-dos-puntos\"><\/span> Calcule a equa\u00e7\u00e3o expl\u00edcita da reta que passa por dois pontos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um problema muito t\u00edpico \u00e9 encontrar a equa\u00e7\u00e3o expl\u00edcita de uma reta dados dois pontos pelos quais ela passa. Vamos ver como isso \u00e9 resolvido atrav\u00e9s de um exemplo:<\/p>\n<ul>\n<li> Determine a equa\u00e7\u00e3o expl\u00edcita da reta que passa pelos dois pontos a seguir:<\/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-5dc040b45ee8f50d03d1b63ba807046b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(4,-1) \\qquad P_2(2,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para encontrar a equa\u00e7\u00e3o expl\u00edcita da reta, voc\u00ea precisa saber quanto valem os par\u00e2metros m e n. Ent\u00e3o, primeiro calculamos a inclina\u00e7\u00e3o da reta usando a f\u00f3rmula dos dois pontos:<\/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-cba7b5e777996cf9f1046c8cc473a63d_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{5-(-1)}{2-4} = \\cfrac{6}{-2}= -3\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"336\" style=\"vertical-align: -15px;\"><\/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-5cac49aacff5d5cd3c83c013484090f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-3x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> E ent\u00e3o podemos encontrar a intercepta\u00e7\u00e3o y substituindo um ponto na reta na equa\u00e7\u00e3o: <\/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-4b1925eb0d625bf10df649d785dc15b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/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-fd572396259e812490230062fd6b6ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -3x+n \\ \\xrightarrow{x=4 \\ ; \\ y=-1} \\ -1=-3\\cdot 4 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"330\" style=\"vertical-align: -4px;\"><\/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-728ab1485d8074270339b6715ca5956f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1 =-12+ n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" style=\"vertical-align: -2px;\"><\/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-a0e23ee0e60bc28f13720f1bd39a6e1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1 +12= n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\"><\/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-b1c6ccd71a491da3f0ba05f00a111bf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"11= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Portanto, a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9: <\/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-dc0f2b352e301360f1a95002bab35877_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=-3x+11}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"104\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-la-ecuacion-explicita-a-partir-de-la-ecuacion-implicita\"><\/span> Encontrando a equa\u00e7\u00e3o expl\u00edcita a partir da equa\u00e7\u00e3o impl\u00edcita<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Finalmente, outro tipo de problema que frequentemente encontramos \u00e9 encontrar a equa\u00e7\u00e3o expl\u00edcita da reta a partir de sua equa\u00e7\u00e3o impl\u00edcita (tamb\u00e9m chamada de equa\u00e7\u00e3o geral ou cartesiana). Obviamente, para entender o m\u00e9todo a seguir voc\u00ea precisa saber exatamente qual \u00e9 a <a href=\"https:\/\/mathority.org\/pt\/equacao-cartesiana-geral-ou-implicita-de-uma-reta\/\">equa\u00e7\u00e3o impl\u00edcita<\/a> e como ela \u00e9; mas se voc\u00ea n\u00e3o se lembra de nada, pode conferir no link.<\/p>\n<p> Ent\u00e3o, se voc\u00ea j\u00e1 domina a equa\u00e7\u00e3o impl\u00edcita (ou geral) de uma reta, vamos ver como funciona esse procedimento:<\/p>\n<ul>\n<li> Encontre a equa\u00e7\u00e3o expl\u00edcita da seguinte reta:<\/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-c6216b116c172719854040288742a2bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-2y+8 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"122\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Tudo o que precisamos fazer para encontrar a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9 <strong>resolver a vari\u00e1vel<\/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-98853ed03118bfa073ac5183999ded53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y}.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> Ent\u00e3o passamos os termos sem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> do outro lado da equa\u00e7\u00e3o:<\/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-a095dec8af4b30fcb4dd41766a6065d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2y=-3x-8\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Agora limpamos a vari\u00e1vel<\/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-526e84c5b87e970b9045246e059785fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/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-c488fd96d556056e36c5cecd1b1d109c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=\\frac{-3x-8}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"99\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> E finalmente simplificamos: <\/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-9460a7221d8d649a4bcf6af275c54868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=\\frac{-3x}{-2} -\\cfrac{8}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" style=\"vertical-align: -12px;\"><\/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-95c3b7d67756ee77a8688cab43936d67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=\\frac{3x}{2} -(-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"114\" style=\"vertical-align: -12px;\"><\/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-d89d435224477ab13ef0432e17ac6cd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{y=}\\frac{\\bm{3}}{\\bm{2}}\\bm{x +4}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"82\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> A inclina\u00e7\u00e3o desta reta \u00e9 portanto<\/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-8e9b7a81649daeb4cc6d1df49cceb46d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"><\/p>\n<p> e sua intercepta\u00e7\u00e3o em y \u00e9 4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-ecuacion-explicita\"><\/span> Problemas de equa\u00e7\u00f5es expl\u00edcitas resolvidos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> D\u00ea a inclina\u00e7\u00e3o e a intercepta\u00e7\u00e3o em y das seguintes retas: <\/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-3077643710747855c7b59a93551fbad8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{lll} A) \\ y= 3x-1 &amp; \\qquad &amp; B) \\ y=5x+2 \\\\[2ex] C) \\ y=-x+3 &amp; \\qquad &amp; D) \\ 4x+2y-6=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"332\" 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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> A equa\u00e7\u00e3o expl\u00edcita de uma reta segue a seguinte f\u00f3rmula:<\/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-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ouro<\/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> \u00e9 a inclina\u00e7\u00e3o e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> o computador na origem. Ainda: <\/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-f62bc45bc23ea6c323b1a5d95ba40ca2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{A)} \\ y= 3x-1 \\ \\begin{cases} m = 3 \\\\[2ex] n=-1\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"178\" 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-683f74baf43275be7565fc744704e6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{B)} \\ y= 5x+2 \\ \\begin{cases} m = 5 \\\\[2ex] n=2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"176\" 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-39e8a1c6dbe8e5ff8db1fc8b08c4c95d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{C)} \\ y= -x+3 \\ \\begin{cases} m = -1 \\\\[2ex] n=3\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"187\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> A \u00faltima reta \u00e9 expressa por sua equa\u00e7\u00e3o impl\u00edcita, ent\u00e3o primeiro precisamos pass\u00e1-la para uma equa\u00e7\u00e3o expl\u00edcita (resolver para<\/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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> ) ent\u00e3o podemos identificar os par\u00e2metros: <\/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-24b4a6eb6e1ebb9759f462cf3dd3a3b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{D)} \\ 4x+2y-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\"><\/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-dc742016a9d8d6d2d3984bb1e64c6769_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y =-4x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\"><\/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-add487089a6729d77d501cd35a080021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =\\cfrac{-4x+6}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"107\" style=\"vertical-align: -12px;\"><\/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-f4a38e7e5a2d3c03793c933a3fc70418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =-2x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\"><\/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-50c2bb75ae362e0a2dee3a3670459df3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases} m = -2 \\\\[2ex] n=3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 2<\/h3>\n<p> Encontre a equa\u00e7\u00e3o expl\u00edcita da reta que passa pelo ponto<\/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-c0dcab0961089b0aa76f0425102b9e92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p> e tem a inclina\u00e7\u00e3o <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e3505d96cc978cbd5e9fefda94605f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=-2.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" 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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> A f\u00f3rmula para a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9:<\/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-c8bbb40f6658cea3b5ba541c3fbde45f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Neste caso, a inclina\u00e7\u00e3o da reta deve ser -2, ent\u00e3o a equa\u00e7\u00e3o da reta ter\u00e1 a seguinte forma:<\/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-e01b49b9364c6df049137d5cd885fb55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -2x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"98\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u00c9, portanto, suficiente calcular o coeficiente n. Para fazer isso, voc\u00ea deve substituir um ponto pertencente \u00e0 reta em sua equa\u00e7\u00e3o e resolver a equa\u00e7\u00e3o resultante: <\/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-c0dcab0961089b0aa76f0425102b9e92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/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-10bd3d68c93e4dd1552ef11b32a0fe70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -2x+n \\ \\xrightarrow{x=2 \\ ; \\ y=-3} \\ -3=-2\\cdot 2 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"330\" style=\"vertical-align: -4px;\"><\/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-f3c26b085cc22c32165d4690b95429c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3=-4 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"101\" style=\"vertical-align: -2px;\"><\/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-af613be447206c3a89ad768c14f0836d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3+4= n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -2px;\"><\/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-a2faaed401a68778015b498a664021f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Resumindo, a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9: <\/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-86e5317d333f23b00e8000d7ec04af3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y= -2x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 3<\/h3>\n<p> Encontre a equa\u00e7\u00e3o expl\u00edcita da reta que passa pelos dois pontos a seguir: <\/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-434c91cced129df5e0a84239ebc2b510_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(6,-1) \\qquad P_2(3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar a equa\u00e7\u00e3o expl\u00edcita da reta, voc\u00ea precisa saber quanto valem os par\u00e2metros m e n. Portanto, primeiro calculamos a inclina\u00e7\u00e3o da reta a partir das coordenadas dos dois pontos: <\/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-672cce907f46f56289e0e9cc16d47999_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{2-(-1)}{3-6} = \\cfrac{3}{-3}= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"335\" style=\"vertical-align: -15px;\"><\/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-c726950f4d4e6cbd4d9bbe347658b005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E ent\u00e3o determinamos a intercepta\u00e7\u00e3o substituindo um ponto da reta na equa\u00e7\u00e3o: <\/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-e53a51b9f343c0601351fdd739e33807_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1(6,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/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-38f34cd52cc58989827a959a578a8fa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -x+n \\ \\xrightarrow{x=6 \\ ; \\ y=-1} \\ -1=-6 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"300\" style=\"vertical-align: -4px;\"><\/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-e3de573ad286cffa3c5ac2e265048adf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1 +6= n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -2px;\"><\/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-176b8f547a6bb3859a36ec2955887bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5= n\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Portanto, a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9: <\/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-0e9c8c3bca3af560065f336cc67d5d10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=-x+5}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"87\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 4<\/h3>\n<p> Calcule a equa\u00e7\u00e3o expl\u00edcita da reta que forma um \u00e2ngulo de 45\u00ba com o eixo X e passa pela origem das coordenadas. <\/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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Se a linha fizer um \u00e2ngulo de 45 graus com o eixo OX, sua inclina\u00e7\u00e3o ser\u00e1: <\/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-51d113bc9a4b67f4c35c31f08baa7ad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}(45\u00ba) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\"><\/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-59a41473d4f1a3eda1d2f0b0bd242cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"76\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E uma vez que conhecemos o declive da reta, podemos calcular a interse\u00e7\u00e3o y substituindo um ponto da reta na equa\u00e7\u00e3o. Al\u00e9m disso, a afirma\u00e7\u00e3o nos diz que a reta passa pela origem das coordenadas, o que significa que ela passa pelo ponto (0,0). Ainda: <\/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-048c1ceefde62a60b4cf2420a67d7f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/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-3a0e59d3a0d2a22a736745d245e415be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= x+n \\ \\xrightarrow{x=0 \\ ; \\ y=0} \\ 0=0 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"248\" style=\"vertical-align: -4px;\"><\/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-ecfe55263dbd4ec64b27a771a1b26a28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Portanto, a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9: <\/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-4909df7491ef54f0df1e922bc29417f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=x}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 5<\/h3>\n<p> Encontre a equa\u00e7\u00e3o expl\u00edcita da reta paralela \u00e0 reta<\/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-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> e o que acontece al\u00e9m do ponto<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca1267dd7cc3383841205c68c87dfb16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,4).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<p> ser direto <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-4f08054b86ce89eea1f92b97a4e32cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\; y=3x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"111\" style=\"vertical-align: -4px;\"><\/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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para que a linha seja paralela \u00e0 linha<\/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-42ca8c420951296e93092e708435813a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> ambos devem ter a mesma inclina\u00e7\u00e3o, portanto: <\/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-0082d45adbb746641eb28f250a819459_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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4def7be28b405258061bd824635dc80e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=3x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E uma vez que conhecemos a inclina\u00e7\u00e3o da reta, podemos calcular a intercepta\u00e7\u00e3o y substituindo o ponto que pertence \u00e0 reta na equa\u00e7\u00e3o: <\/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-67b8a26e3dd7234279553321372645bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/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-d894f378de0e275883f2039ec0a6f088_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= 3x+n \\ \\xrightarrow{x=-2 \\ ; \\ y=4} \\ 4=3\\cdot (-2) +n\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"316\" style=\"vertical-align: -5px;\"><\/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-9c9b39f3d5c90e09e45a7c8de9b4bac1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4=-6+ n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"88\" style=\"vertical-align: -2px;\"><\/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-be0cc26e3d897a12f92e01d37a461b8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4+6= n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"74\" style=\"vertical-align: -2px;\"><\/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-bc5ca740c7ca9e561adfcb7d08ae7dca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"10= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Portanto, a equa\u00e7\u00e3o expl\u00edcita da reta \u00e9: <\/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-92c543f9f049c064fd01d105a5d5bd8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=3x+10}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 6<\/h3>\n<p> Qual \u00e9 a equa\u00e7\u00e3o expl\u00edcita de cada linha representada graficamente? <\/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=\"equa\u00e7\u00e3o expl\u00edcita da linha exerc\u00edcio resolvido passo a passo\" 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>veja solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>azul \u00e0 direita<\/strong><\/p>\n<p class=\"has-text-align-left\"> A linha azul aumenta um Y para cada<\/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-6f354cad2de2c83534811996e7055b2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>verde direito<\/strong><\/p>\n<p class=\"has-text-align-left\"> A linha verde aumenta em 3 Ys para cada X, ent\u00e3o sua inclina\u00e7\u00e3o \u00e9 3. Al\u00e9m disso, a linha cruza o eixo Y em -4, ent\u00e3o sua intercepta\u00e7\u00e3o em y \u00e9 -4.<\/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-c2d3fa8208699a24dc4372aefc321fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =3x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>Linha Vermelha<\/strong><\/p>\n<p class=\"has-text-align-left\"> A linha vermelha diminui em dois Y para cada X, ent\u00e3o sua inclina\u00e7\u00e3o \u00e9 -2. E a reta intercepta o eixo y em y=-2, ent\u00e3o sua intercepta\u00e7\u00e3o em y tamb\u00e9m \u00e9 -2. <\/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-89d5c40c97036a10235c83942a45b036_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y =-2x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a equa\u00e7\u00e3o expl\u00edcita de uma reta: o que \u00e9, qual a sua f\u00f3rmula, exemplos de c\u00e1lculo, etc. Voc\u00ea tamb\u00e9m encontrar\u00e1 uma explica\u00e7\u00e3o detalhada do que significa inclina\u00e7\u00e3o e a intercepta\u00e7\u00e3o da equa\u00e7\u00e3o expl\u00edcita. E, al\u00e9m disso, voc\u00ea ver\u00e1 diversos exemplos e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\"> <span class=\"screen-reader-text\">Equa\u00e7\u00e3o expl\u00edcita da reta<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[20],"tags":[],"class_list":["post-224","post","type-post","status-publish","format-standard","hentry","category-pontos-retas-e-planos"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equa\u00e7\u00e3o expl\u00edcita da reta - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equa\u00e7\u00e3o expl\u00edcita da reta - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 tudo sobre a equa\u00e7\u00e3o expl\u00edcita de uma reta: o que \u00e9, qual a sua f\u00f3rmula, exemplos de c\u00e1lculo, etc. Voc\u00ea tamb\u00e9m encontrar\u00e1 uma explica\u00e7\u00e3o detalhada do que significa inclina\u00e7\u00e3o e a intercepta\u00e7\u00e3o da equa\u00e7\u00e3o expl\u00edcita. E, al\u00e9m disso, voc\u00ea ver\u00e1 diversos exemplos e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. &hellip; Equa\u00e7\u00e3o expl\u00edcita da reta Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T23:45:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Equa\u00e7\u00e3o expl\u00edcita da reta\",\"datePublished\":\"2023-07-10T23:45:14+00:00\",\"dateModified\":\"2023-07-10T23:45:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\"},\"wordCount\":540,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Pontos, retas e planos\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\",\"url\":\"https:\/\/mathority.org\/pt\/equacao-explicita-de-uma-reta\/\",\"name\":\"Equa\u00e7\u00e3o expl\u00edcita da reta - 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