{"id":269,"date":"2023-07-10T23:45:14","date_gmt":"2023-07-10T23:45:14","guid":{"rendered":"https:\/\/mathority.org\/nl\/expliciete-vergelijking-van-een-lijn\/"},"modified":"2023-07-10T23:45:14","modified_gmt":"2023-07-10T23:45:14","slug":"expliciete-vergelijking-van-een-lijn","status":"publish","type":"post","link":"https:\/\/mathority.org\/nl\/expliciete-vergelijking-van-een-lijn\/","title":{"rendered":"Expliciete vergelijking van de lijn"},"content":{"rendered":"<p>Op deze pagina vindt u alles over de expliciete vergelijking van een lijn: wat is het, wat is de formule, rekenvoorbeelden, enz. U vindt ook een gedetailleerde uitleg van wat helling betekent en het snijpunt van de expliciete vergelijking. En bovendien krijg je verschillende voorbeelden te zien en kun je oefenen met oefeningen die stap voor stap worden opgelost. <\/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> Wat is de expliciete vergelijking van de lijn?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bedenk dat de wiskundige definitie van een lijn een reeks opeenvolgende punten is die in dezelfde richting worden weergegeven, zonder krommen of hoeken. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> De <strong>expliciete lijnvergelijking<\/strong> is dus een manier om elke lijn wiskundig uit te drukken. Om dit te doen, hoeft u alleen maar de <a href=\"https:\/\/mathority.org\/nl\/helling-van-de-lijnformule\/\">helling van de lijn<\/a> te kennen en het punt waar deze de Y-as snijdt. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-ecuacion-explicita-de-la-recta\"><\/span> Formule voor de expliciete vergelijking van de lijn <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\"> De formule voor de <strong>expliciete vergelijking van de lijn<\/strong> is:<\/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;\"> Goud<\/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> is de helling van de lijn en<\/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> het y-snijpunt, dat wil zeggen de hoogte waarop het de Y-as snijdt. <\/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> Laten we eens kijken <strong>hoe de expliciete vergelijking van de lijn wordt berekend<\/strong> aan de hand van een voorbeeld:<\/p>\n<ul>\n<li> Schrijf de expliciete vergelijking van de lijn die door het punt gaat\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> en helling m=2.<\/li>\n<\/ul>\n<p> De formule voor de expliciete vergelijking van de lijn is:<\/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 dit geval vertelt de verklaring ons dat de helling van de lijn m=2 is, dus de vergelijking van de lijn zal als volgt zijn:<\/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> Het is daarom voldoende om de co\u00ebffici\u00ebnt n te berekenen. Om dit te doen, moeten we een punt dat bij de lijn hoort in de vergelijking vervangen. En in dit geval vertelt de verklaring ons dat de lijn door het punt gaat<\/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> Nog:<\/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> En we lossen de resulterende vergelijking op om de waarde van n te vinden: <\/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> De expliciete vergelijking van de lijn is daarom:<\/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> Houd er rekening mee dat er naast de expliciete vergelijking ook andere manieren zijn om een lijn analytisch uit te drukken. Bijvoorbeeld de <a href=\"https:\/\/mathority.org\/nl\">vectorvergelijking<\/a> , een soort lijnvergelijking die verschilt van alle andere omdat de richtingsvector en een punt op de lijn worden uitgedrukt met hun eigen co\u00f6rdinaten. In de link zie je wat het is en waarom het zo bijzonder is. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"significado-de-los-parametros-m-y-n\"><\/span> Betekenis van parameters m en 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> Zoals we zagen bij de definitie van de expliciete vergelijking van de lijn, de parameter<\/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> is de helling van de lijn en<\/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> het y-snijpunt. Maar wat betekent dat? Laten we dit eens bekijken aan de hand van de grafische weergave van een lijn: <\/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=\"Wat is de expliciete vergelijking van de lijn y=mx+b\" class=\"wp-image-1455\" width=\"339\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> De term onafhankelijk<\/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>is het snijpunt van de lijn met de computeras<\/strong> (OY-as). In de grafiek hierboven<\/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> is gelijk aan 1 omdat de lijn de y-as snijdt op y=1.<\/p>\n<p> Aan de andere kant, de term<\/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>geeft de helling van de lijn aan<\/strong> , dat wil zeggen de helling ervan. Zoals je in de grafiek ziet,<\/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> is gelijk aan 2 omdat de lijn 2 verticale eenheden stijgt voor 1 horizontale eenheid.<\/p>\n<p> Het is duidelijk dat als de helling positief is, de functie toeneemt (omhoog), maar als de helling negatief is, neemt de functie af (omlaag).<\/p>\n<h4 class=\"wp-block-heading\"> Bereken de helling van een lijn<\/h4>\n<p> Verder zijn er 3 verschillende manieren om de helling van een lijn numeriek te bepalen:<\/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;\">Gegeven twee verschillende punten op de lijn\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> En<\/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> De helling van de lijn is gelijk aan:<\/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;\">Ja\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> is de richtingsvector van de lijn, de helling is:<\/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;\">Ja\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> is de hoek gevormd door de lijn met de abscis-as (X-as), de helling van de lijn is gelijk aan de raaklijn van genoemde hoek: <\/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=\"formule voor de expliciete vergelijking van de lijn\" class=\"wp-image-1465\" width=\"288\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\"> Relatieve positie van lijnen<\/h4>\n<p> Ten slotte wordt de helling van een lijn ook gebruikt om de relatie tussen verschillende lijnen te kennen. Omdat twee <strong>parallelle<\/strong> lijnen dezelfde helling hebben en, aan de andere kant, als de helling van \u00e9\u00e9n lijn het negatieve omgekeerde is van de helling van een andere lijn, betekent dit dat deze twee lijnen <strong>loodrecht<\/strong> staan. <\/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=\"evenwijdige lijnen met dezelfde helling\" 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> Bereken de expliciete vergelijking van de lijn die door twee punten gaat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Een heel typisch probleem is het vinden van de expliciete vergelijking van een lijn gegeven twee punten waar deze doorheen gaat. Laten we eens kijken hoe het wordt opgelost aan de hand van een voorbeeld:<\/p>\n<ul>\n<li> Bepaal de expliciete vergelijking van de lijn die door de volgende twee punten gaat:<\/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> Om de expliciete vergelijking van de lijn te vinden, moet je weten wat de parameters m en n waard zijn. We berekenen dus eerst de helling van de lijn met behulp van de dubbele puntformule:<\/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> En dan kunnen we het y-snijpunt vinden door een punt op de lijn in de vergelijking te vervangen: <\/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> Dus de expliciete vergelijking van de lijn is: <\/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> Het vinden van de expliciete vergelijking uit de impliciete vergelijking<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Een ander type probleem dat we vaak tegenkomen, is het vinden van de expliciete vergelijking van de lijn op basis van de impliciete vergelijking ervan (ook wel een algemene of cartesiaanse vergelijking genoemd). Om de volgende methode te begrijpen, moet je uiteraard precies weten wat de <a href=\"https:\/\/mathority.org\/nl\/algemene-of-impliciete-cartesiaanse-vergelijking-van-een-lijn\/\">impliciete vergelijking<\/a> is en hoe deze is; maar als je het helemaal niet meer weet, kun je het via de link bekijken.<\/p>\n<p> Dus, als je de impliciete (of algemene) vergelijking van een lijn al onder de knie hebt, laten we dan eens kijken hoe deze procedure werkt:<\/p>\n<ul>\n<li> Zoek de expliciete vergelijking van de volgende regel:<\/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> Het enige wat we hoeven te doen om de expliciete vergelijking van de lijn te vinden, is <strong>het oplossen van de variabele<\/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> Dus we passeren de voorwaarden zonder<\/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> aan de andere kant van de vergelijking:<\/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> Nu wissen we de variabele<\/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> En tot slot vereenvoudigen we: <\/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> De helling van deze lijn is dus<\/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> en het y-snijpunt is 4. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-ecuacion-explicita\"><\/span> Opgeloste expliciete vergelijkingsproblemen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Oefening 1<\/h3>\n<p> Geef de helling en het y-snijpunt van de volgende lijnen: <\/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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> De expliciete vergelijking van een lijn volgt de volgende formule:<\/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\"> Goud<\/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> is de helling en<\/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> de computer bij de oorsprong. Nog: <\/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\"> De laatste regel wordt uitgedrukt door de impliciete vergelijking ervan, dus we moeten deze eerst doorgeven aan een expliciete vergelijking (oplossen voor<\/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> ) dan kunnen we de parameters identificeren: <\/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\">Oefening 2<\/h3>\n<p> Zoek de expliciete vergelijking van de lijn die door het punt gaat<\/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> en heeft de helling <\/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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> De formule voor de expliciete vergelijking van de lijn is:<\/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 dit geval moet de helling van de lijn -2 zijn, dus de vergelijking van de lijn heeft de volgende vorm:<\/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\"> Het is daarom voldoende om de co\u00ebffici\u00ebnt n te berekenen. Om dit te doen, moet je een punt dat bij de lijn hoort in de vergelijking vervangen en de resulterende vergelijking oplossen: <\/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\"> Kortom, de expliciete vergelijking van de lijn is: <\/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\">Oefening 3<\/h3>\n<p> Zoek de expliciete vergelijking van de lijn die door de volgende twee punten gaat: <\/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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Om de expliciete vergelijking van de lijn te vinden, moet je weten wat de parameters m en n waard zijn. We berekenen daarom eerst de helling van de lijn op basis van de co\u00f6rdinaten van de twee punten: <\/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\"> En dan bepalen we het snijpunt door een punt op de lijn in de vergelijking te vervangen: <\/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\"> Dus de expliciete vergelijking van de lijn is: <\/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\">Oefening 4<\/h3>\n<p> Bereken de expliciete vergelijking van de lijn die een hoek van 45\u00ba vormt met de X-as en door de oorsprong van de co\u00f6rdinaten gaat. <\/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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Als de lijn een hoek van 45 graden maakt met de OX-as, is de helling: <\/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\"> En zodra we de helling van de lijn kennen, kunnen we het y-snijpunt berekenen door een punt op de lijn in de vergelijking te vervangen. Bovendien vertelt de verklaring ons dat de lijn door de co\u00f6rdinaatoorsprong gaat, wat betekent dat deze door het punt (0,0) gaat. Nog: <\/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\"> Dus de expliciete vergelijking van de lijn is: <\/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\">Oefening 5<\/h3>\n<p> Zoek de expliciete vergelijking van de lijn evenwijdig aan de lijn<\/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> en wat er aan de overkant gebeurt<\/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> eerlijk zijn <\/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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Zodat de lijn evenwijdig is aan de lijn<\/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> beide moeten dezelfde helling hebben, daarom: <\/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\"> En zodra we de helling van de lijn kennen, kunnen we het y-snijpunt berekenen door het punt dat bij de lijn hoort in de vergelijking te vervangen: <\/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\"> Dus de expliciete vergelijking van de lijn is: <\/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\">Oefening 6<\/h3>\n<p> Wat is de expliciete vergelijking van elke getekende lijn? <\/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=\"expliciete vergelijking van de lijnoefening stap voor stap opgelost\" 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>zie oplossing<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong>blauw rechts<\/strong><\/p>\n<p class=\"has-text-align-left\"> De blauwe lijn wordt voor elk met \u00e9\u00e9n Y verhoogd<\/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>rechts groen<\/strong><\/p>\n<p class=\"has-text-align-left\"> De groene lijn wordt voor elke X met 3 Ys groter, dus de helling is 3. Bovendien snijdt de lijn de Y-as op -4, dus het snijpunt met de y is -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>rode lijn<\/strong><\/p>\n<p class=\"has-text-align-left\"> De rode lijn neemt voor elke X met twee Y af, dus de helling is -2. En de lijn snijdt de y-as op y=-2, dus het y-snijpunt is ook -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>Op deze pagina vindt u alles over de expliciete vergelijking van een lijn: wat is het, wat is de formule, rekenvoorbeelden, enz. U vindt ook een gedetailleerde uitleg van wat helling betekent en het snijpunt van de expliciete vergelijking. En bovendien krijg je verschillende voorbeelden te zien en kun je oefenen met oefeningen die stap &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/nl\/expliciete-vergelijking-van-een-lijn\/\"> <span class=\"screen-reader-text\">Expliciete vergelijking van de lijn<\/span> Lees meer &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":[47],"tags":[],"class_list":["post-269","post","type-post","status-publish","format-standard","hentry","category-punten-lijnen-en-vlakken"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Expliciete vergelijking van de lijn - 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\/nl\/expliciete-vergelijking-van-een-lijn\/\" \/>\n<meta property=\"og:locale\" content=\"nl_NL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Expliciete vergelijking van de lijn - Mathority\" \/>\n<meta property=\"og:description\" content=\"Op deze pagina vindt u alles over de expliciete vergelijking van een lijn: wat is het, wat is de formule, rekenvoorbeelden, enz. 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