{"id":228,"date":"2023-07-10T23:45:14","date_gmt":"2023-07-10T23:45:14","guid":{"rendered":"https:\/\/mathority.org\/it\/equazione-esplicita-di-una-retta\/"},"modified":"2023-07-10T23:45:14","modified_gmt":"2023-07-10T23:45:14","slug":"equazione-esplicita-di-una-retta","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/equazione-esplicita-di-una-retta\/","title":{"rendered":"Equazione esplicita della retta"},"content":{"rendered":"<p>In questa pagina troverai tutto sull&#8217;equazione esplicita di una retta: cos&#8217;\u00e8, qual \u00e8 la sua formula, esempi di calcolo, ecc. Troverai anche una spiegazione dettagliata di cosa significa pendenza e l&#8217;intercetta dell&#8217;equazione esplicita. Inoltre, vedrai diversi esempi e potrai esercitarti con esercizi risolti passo dopo 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 \u00e8 l&#8217;equazione esplicita della retta?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ricorda che la definizione matematica di linea \u00e8 un insieme di punti consecutivi rappresentati nella stessa direzione senza curve o angoli. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Quindi, l&#8217; <strong>equazione esplicita della linea<\/strong> \u00e8 un modo per esprimere matematicamente qualsiasi linea. Per fare ci\u00f2 basta conoscere la <a href=\"https:\/\/mathority.org\/it\/formula-della-pendenza-della-retta\/\">pendenza della retta<\/a> e il punto in cui questa interseca l&#8217;asse Y. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-explicita-de-la-recta\"><\/span> Formula per l&#8217;equazione esplicita della retta <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\"> La formula per l&#8217; <strong>equazione esplicita della retta<\/strong> \u00e8:<\/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;\"> Oro<\/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> \u00e8 la pendenza della retta 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> la sua intercetta y, cio\u00e8 l&#8217;altezza alla quale interseca l&#8217;asse 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> Vediamo <strong>come viene calcolata l&#8217;equazione esplicita della retta<\/strong> attraverso un esempio:<\/p>\n<ul>\n<li> Scrivi l&#8217;equazione esplicita della retta passante per il punto\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 pendenza m=2.<\/li>\n<\/ul>\n<p> La formula per l&#8217;equazione esplicita della retta \u00e8:<\/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> In questo caso, l&#8217;affermazione ci dice che la pendenza della retta \u00e8 m=2, quindi l&#8217;equazione della retta sar\u00e0 la seguente:<\/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> \u00c8 quindi sufficiente calcolare il coefficiente n. Per fare ci\u00f2 dobbiamo sostituire nella sua equazione un punto che appartiene alla retta. E in questo caso l&#8217;enunciato ci dice che la retta passa per il punto<\/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> Ancora:<\/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 risolviamo l&#8217;equazione risultante per trovare il valore di 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> L\u2019equazione esplicita della retta \u00e8 quindi:<\/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> Tieni presente che oltre all&#8217;equazione esplicita, ci sono altri modi per esprimere analiticamente una linea. Ad esempio, l&#8217; <a href=\"https:\/\/mathority.org\/it\">equazione vettoriale<\/a> , che \u00e8 un tipo di equazione della linea diversa da tutte le altre perch\u00e9 il vettore direzione e un punto sulla linea sono espressi con le proprie coordinate. Nel link potete vedere di cosa si tratta e perch\u00e9 \u00e8 cos\u00ec speciale. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"significado-de-los-parametros-m-y-n\"><\/span> Significato dei parametri 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> Come abbiamo visto nella definizione dell&#8217;equazione esplicita della retta, il parametro<\/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> \u00e8 la pendenza della retta 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> la sua intercetta y. Ma cosa significa? Vediamolo dalla rappresentazione grafica di una linea: <\/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 \u00e8 l'equazione esplicita della retta y=mx+b\" class=\"wp-image-1455\" width=\"339\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Il termine indipendente<\/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>\u00e8 il punto di intersezione della linea con l&#8217;asse del computer<\/strong> (asse OY). Nel grafico sopra<\/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> \u00e8 uguale a 1 perch\u00e9 la linea interseca l&#8217;asse y in y=1.<\/p>\n<p> D&#8217;altra parte, il termine<\/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 la pendenza della retta<\/strong> , cio\u00e8 la sua inclinazione. Come vedi nel grafico,<\/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> \u00e8 uguale a 2 poich\u00e9 la linea sale di 2 unit\u00e0 verticali per 1 unit\u00e0 orizzontale.<\/p>\n<p> Ovviamente se la pendenza \u00e8 positiva la funzione \u00e8 crescente (sale), invece se la pendenza \u00e8 negativa la funzione \u00e8 decrescente (scende).<\/p>\n<h4 class=\"wp-block-heading\"> Calcolare la pendenza di una retta<\/h4>\n<p> Inoltre, ci sono 3 modi diversi per determinare numericamente la pendenza di una linea:<\/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;\">Dati due punti diversi sulla retta\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> La pendenza della retta \u00e8 pari 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;\">S\u00ec\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> \u00e8 il vettore direzione della retta, la sua pendenza \u00e8:<\/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;\">S\u00ec\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> \u00e8 l&#8217;angolo formato dalla retta con l&#8217;asse delle ascisse (asse X), la pendenza della retta \u00e8 equivalente alla tangente di detto angolo: <\/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=\"formula per l'equazione esplicita della retta\" class=\"wp-image-1465\" width=\"288\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\"> Posizione relativa delle linee<\/h4>\n<p> Infine, la pendenza di una linea viene utilizzata anche per conoscere la relazione tra pi\u00f9 linee. Poich\u00e9 due rette <strong>parallele<\/strong> hanno la stessa pendenza e, d&#8217;altra parte, se la pendenza di una retta \u00e8 l&#8217;inverso negativo della pendenza di un&#8217;altra retta, ci\u00f2 significa che queste due rette sono <strong>perpendicolari<\/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=\"rette parallele con la stessa pendenza\" 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> Calcola l&#8217;equazione esplicita della retta che passa per due punti<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Un problema molto tipico \u00e8 trovare l&#8217;equazione esplicita di una retta dati due punti per i quali passa. Vediamo come si risolve attraverso un esempio:<\/p>\n<ul>\n<li> Determinare l&#8217;equazione esplicita della retta che passa per i seguenti due punti:<\/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> Per trovare l&#8217;equazione esplicita della retta, devi sapere quanto valgono i parametri m e n. Quindi calcoliamo prima la pendenza della linea usando la formula dei due punti:<\/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 poi possiamo trovare l&#8217;intercetta y sostituendo un punto sulla linea nell&#8217;equazione: <\/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> Quindi l&#8217;equazione esplicita della retta \u00e8: <\/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> Trovare l&#8217;equazione esplicita dall&#8217;equazione implicita<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Infine, un altro tipo di problema che incontriamo spesso \u00e8 trovare l&#8217;equazione esplicita della retta a partire dalla sua equazione implicita (chiamata anche equazione generale o cartesiana). Ovviamente, per comprendere il seguente metodo \u00e8 necessario sapere esattamente qual \u00e8 l&#8217; <a href=\"https:\/\/mathority.org\/it\/equazione-cartesiana-generale-o-implicita-di-una-retta\/\">equazione implicita<\/a> e come \u00e8; ma se non lo ricordi affatto, puoi verificarlo nel link.<\/p>\n<p> Quindi, se conosci gi\u00e0 l&#8217;equazione implicita (o generale) di una linea, vediamo come funziona questa procedura:<\/p>\n<ul>\n<li> Trova l&#8217;equazione esplicita della seguente riga:<\/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> Tutto quello che dobbiamo fare per trovare l&#8217;equazione esplicita della retta \u00e8 <strong>risolvere la variabile<\/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> Quindi passiamo i termini senza<\/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> dall&#8217;altra parte dell&#8217;equazione:<\/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> Ora cancelliamo la variabile<\/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> Ed infine semplifichiamo: <\/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> La pendenza di questa retta \u00e8 quindi<\/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 la sua intercetta y \u00e8 4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-ecuacion-explicita\"><\/span> Risolti problemi di equazioni esplicite<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Esercizio 1<\/h3>\n<p> Indica la pendenza e l&#8217;intercetta y delle seguenti rette: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> L&#8217;equazione esplicita di una retta segue la seguente formula:<\/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\"> Oro<\/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> \u00e8 la pendenza 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> il computer all&#8217;origine. Ancora: <\/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\"> L&#8217;ultima riga \u00e8 espressa dalla sua equazione implicita, quindi dobbiamo prima passarla a un&#8217;equazione esplicita (solve for<\/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> ) allora possiamo identificare i parametri: <\/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\">Esercizio 2<\/h3>\n<p> Trova l&#8217;equazione esplicita della retta passante per il punto<\/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 ha la pendenza <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> La formula per l&#8217;equazione esplicita della retta \u00e8:<\/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\"> In questo caso la pendenza della retta deve essere -2, quindi l&#8217;equazione della retta avr\u00e0 la seguente 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\"> \u00c8 quindi sufficiente calcolare il coefficiente n. Per fare ci\u00f2, devi sostituire un punto che appartiene alla linea nella sua equazione e risolvere l&#8217;equazione risultante: <\/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\"> In breve, l\u2019equazione esplicita della retta \u00e8: <\/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\">Esercizio 3<\/h3>\n<p> Trova l&#8217;equazione esplicita della retta che passa per i seguenti due punti: <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Per trovare l&#8217;equazione esplicita della retta, devi sapere quanto valgono i parametri m e n. Calcoliamo quindi prima la pendenza della retta dalle coordinate dei due punti: <\/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 poi determiniamo l&#8217;intercetta sostituendo un punto sulla linea nell&#8217;equazione: <\/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\"> Quindi l&#8217;equazione esplicita della retta \u00e8: <\/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\">Esercizio 4<\/h3>\n<p> Calcola l&#8217;equazione esplicita della retta che forma un angolo di 45\u00ba con l&#8217;asse X e passa per l&#8217;origine delle coordinate. <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Se la retta forma un angolo di 45 gradi con l&#8217;asse OX, la sua pendenza sar\u00e0: <\/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 una volta che conosciamo la pendenza della retta, possiamo calcolare l&#8217;intercetta y sostituendo un punto sulla retta nell&#8217;equazione. Inoltre, l&#8217;affermazione ci dice che la linea passa attraverso l&#8217;origine delle coordinate, il che significa che passa attraverso il punto (0,0). Ancora: <\/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\"> Quindi l&#8217;equazione esplicita della retta \u00e8: <\/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\">Esercizio 5<\/h3>\n<p> Trova l&#8217;equazione esplicita della retta parallela alla retta<\/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 cosa succede oltre questo punto<\/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> essere sincero <\/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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> In modo che la linea sia parallela alla linea<\/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> entrambi devono avere la stessa pendenza, quindi: <\/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 una volta che conosciamo la pendenza della linea, possiamo calcolare l&#8217;intercetta y sostituendo il punto che appartiene alla linea nell&#8217;equazione: <\/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\"> Quindi l&#8217;equazione esplicita della retta \u00e8: <\/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\">Esercizio 6<\/h3>\n<p> Qual \u00e8 l&#8217;equazione esplicita di ciascuna linea graficata? <\/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=\"Equazione esplicita dell'esercizio della retta risolto passo dopo 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>vedi soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>blu a destra<\/strong><\/p>\n<p class=\"has-text-align-left\"> La linea blu aumenta di una Y per ciascuno<\/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 giusto<\/strong><\/p>\n<p class=\"has-text-align-left\"> La linea verde aumenta di 3 Y per ogni X, quindi la sua pendenza \u00e8 3. Inoltre, la linea interseca l&#8217;asse Y a -4, quindi la sua intercetta y \u00e8 -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>linea rossa<\/strong><\/p>\n<p class=\"has-text-align-left\"> La linea rossa diminuisce di due Y per ogni X, quindi la sua pendenza \u00e8 -2. E la linea interseca l&#8217;asse y in y=-2, quindi anche la sua intercetta y \u00e8 -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>In questa pagina troverai tutto sull&#8217;equazione esplicita di una retta: cos&#8217;\u00e8, qual \u00e8 la sua formula, esempi di calcolo, ecc. Troverai anche una spiegazione dettagliata di cosa significa pendenza e l&#8217;intercetta dell&#8217;equazione esplicita. Inoltre, vedrai diversi esempi e potrai esercitarti con esercizi risolti passo dopo passo. Qual \u00e8 l&#8217;equazione esplicita della retta? Ricorda che la &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/equazione-esplicita-di-una-retta\/\"> <span class=\"screen-reader-text\">Equazione esplicita della retta<\/span> Leggi altro &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":[15],"tags":[],"class_list":["post-228","post","type-post","status-publish","format-standard","hentry","category-punti-rette-e-piani"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equazione esplicita della retta - 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\/it\/equazione-esplicita-di-una-retta\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equazione esplicita della retta - Mathority\" \/>\n<meta property=\"og:description\" content=\"In questa pagina troverai tutto sull&#8217;equazione esplicita di una retta: cos&#8217;\u00e8, qual \u00e8 la sua formula, esempi di calcolo, ecc. 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