{"id":164,"date":"2020-01-17T23:49:04","date_gmt":"2020-01-17T23:49:04","guid":{"rendered":"https:\/\/henriksenmatematik.wordpress.com\/?p=164"},"modified":"2026-04-09T22:42:38","modified_gmt":"2026-04-09T20:42:38","slug":"linjens-ligninger","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=164","title":{"rendered":"Linjens Forskellige Former"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Den rette linje kender vi og vi har i grundforl\u00f8bet set p\u00e5 den p\u00e5 formen<\/p>\n\n\n\n<p class=\"has-text-align-center eplus-wrapper\">$y=ax+b$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Men der er andre m\u00e5der, hvor vi matematisk kan beskrive den rette linje. Vi ser her p\u00e5 to andre former, nemlig<\/p>\n\n\n<ul class=\"eplus-wrapper wp-block-list eplus-styles-uid-5ab347\"><li>normalform<\/li><li>parameterfremstilling<\/li><\/ul>\n\n\n<p class=\" eplus-wrapper\">Vi starter med at se p\u00e5 linjens ligning p\u00e5 normalform.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed alignfull is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/C0cMwWganCY?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">En anden m\u00e5de vi kan beskrive en linje p\u00e5 er med vektorer. Denne m\u00e5de at beskrive en ret linje p\u00e5 kaldes for en parameterfremstilling af en linje.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed alignfull is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/79yeku4uzrQ?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Herunder er der en interaktiv \u00f8velse som viser det med dynamiske og statiske vektorer. Her kan du lege lidt med parameterfremstillingen og se hvordan vektorerne ser ud n\u00e5r du \u00e6ndre p\u00e5 parameteren t.<\/p>\n\n\n\n<hr class=\"aligncenter is-style-wide wp-block-separator has-text-color has-foreground-dark-color has-css-opacity has-foreground-dark-background-color has-background eplus-wrapper\"\/>\n\n\n\n<div class=\"wp-block-group alignfull has-background-dark-background-color has-background eplus-wrapper is-layout-flow wp-block-group-is-layout-flow\">\n<h4 class=\"has-text-align-center eplus-wrapper wp-block-heading\"><strong>Interaktiv \u00f8velse<\/strong><\/h4>\n\n\n\n<p style=\"text-align:center\">\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Interaktiv \u00f8velse - parameterfremstilling for en linje\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/vqqzbabg\/width\/1464\/height\/813\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" style=\"border:0px;\" width=\"1464px\" height=\"450px\"> <\/iframe>\n<\/p>\n<\/div>\n\n\n\n<hr class=\"aligncenter is-style-wide wp-block-separator has-text-color has-foreground-dark-color has-css-opacity has-foreground-dark-background-color has-background eplus-wrapper\"\/>\n\n\n\n<p class=\" eplus-wrapper\">Lad os se p\u00e5 et eksempel, hvor vi skal opskrive parameterfremstillingen for en linje og tjekke om et punkt ligger p\u00e5 en linje.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed alignfull is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/ABB4unuhxfM?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Til sidst kan vi lige se p\u00e5 sammenh\u00e6ngen mellem de forskellige former. Specielt hvordan vi finder en retningsvektor ud fra de to andre former.<\/p>\n\n\n\n<figure class=\"wp-embed-aspect-16-9 wp-has-aspect-ratio wp-block-embed alignfull is-type-video is-provider-youtube wp-block-embed-youtube eplus-wrapper\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/m2wrUIFrm_8?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=da-DK&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Den rette linje kender vi og vi har i grundforl\u00f8bet set p\u00e5 den p\u00e5 formen $y=ax+b$ Men der er andre m\u00e5der, hvor vi matematisk kan beskrive den rette linje. Vi ser her p\u00e5 to andre former, nemlig normalform parameterfremstilling Vi starter med at se p\u00e5 linjens ligning p\u00e5 normalform. En anden m\u00e5de vi kan beskrive [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[10,3],"tags":[74],"class_list":["post-164","post","type-post","status-publish","format-standard","hentry","category-analytisk-plangeometri","category-matematik","tag-htx"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=164"}],"version-history":[{"count":4,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions"}],"predecessor-version":[{"id":1847,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions\/1847"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}