{"id":337,"date":"2022-04-13T09:05:28","date_gmt":"2022-04-13T09:05:28","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=337"},"modified":"2025-08-20T01:48:27","modified_gmt":"2025-08-20T01:48:27","slug":"t-20-write-an-equation-for-a-parallel-or-perpendicular-line","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-20-write-an-equation-for-a-parallel-or-perpendicular-line\/","title":{"rendered":"T.20 Write an equation for a parallel or perpendicular line"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#03006f;text-transform:uppercase\"><strong>Write an equation for a parallel or perpendicular line<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwIfK9W94\/Vw9iDz6xWRQWSH8VACGp7w\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwIfK9W94&#x2F;Vw9iDz6xWRQWSH8VACGp7w&#x2F;watch?utm_content=DAGwIfK9W94&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.20 Write an equation for a parallel or perpendicular\u00a0line<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5883468b5790396d423710fbb93a7377\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-3ef87693ecb1aeec238b49448fa909c3\" style=\"color:#000060\"><strong> Recap: Slope-Intercept Form<\/strong><\/h2>\n\n\n\n<p>A line in <strong>slope-intercept form<\/strong> is: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m = slope<\/li>\n\n\n\n<li>b = y-intercept<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-83f7a9b1dd57695c2f4eb72eafa37eac\" style=\"color:#000020\"><strong> Parallel Lines<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rule:<\/strong> Parallel lines have <strong>the same slope<\/strong>.<br>If line 1 has slope <strong>m<\/strong>, then the parallel line also has slope <strong>m.<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>Steps to write the equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the slope <strong>m <\/strong>from the given line.<\/li>\n\n\n\n<li>Use the point you are given that lies on the new line.<\/li>\n\n\n\n<li>Use <strong>point-slope form<\/strong>:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>y\u2212y<sub>1<\/sub>=m(x\u2212x<sub>1<\/sub>)<\/strong><\/p>\n\n\n\n<p>Simplify to slope-intercept form y=mx+b<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Write an equation of a line parallel to y=2x+5 passing through (3, -4).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given slope m=2 (same as original line).<\/li>\n\n\n\n<li>Use point (3, -4): <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">y\u2212(\u22124)=2(x\u22123)<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y+4=2x\u22126<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y=2x\u221210<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-666880b01fe1464c6e2b76aadfab1d40\" style=\"color:#000060\"><strong>Perpendicular Lines<\/strong><\/h2>\n\n\n\n<p><strong>Rule:<\/strong> Perpendicular lines have slopes that are <strong>negative reciprocals<\/strong>: <\/p>\n\n\n\n<p class=\"has-text-align-center\">m1\u00d7m2=\u22121<\/p>\n\n\n\n<p class=\"has-text-align-left\">if m<sub>1<\/sub>\u200b=a, then m<sub>2<\/sub>=\u22121\/a<\/p>\n\n\n\n<p><strong>Steps to write the equation:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the slope of the given line.<\/li>\n\n\n\n<li>Find the <strong>negative reciprocal<\/strong> of that slope for the new line.<\/li>\n\n\n\n<li>Use the given point and the new slope in <strong>point-slope form<\/strong>.<\/li>\n\n\n\n<li>Simplify to slope-intercept form.<\/li>\n<\/ol>\n\n\n\n<p><strong>Example:<\/strong><br>Write an equation of a line perpendicular to y=1\/2x+7 passing through (4, 1).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Given slope m<sub>1<\/sub>=1\/2<\/li>\n\n\n\n<li>Perpendicular slope m<sub>2<\/sub>=\u22122<\/li>\n\n\n\n<li>Use point (4, 1): <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">y\u22121=\u22122(x\u22124)<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y\u22121=\u22122x+8<\/p>\n\n\n\n<p class=\"has-text-align-center\">y = -2x + 9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-71a0c63a7b67d6c319869feec8411ef1\" style=\"color:#000060\"><strong>Special Cases<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>horizontal line<\/strong> (m=0) is perpendicular to a <strong>vertical line<\/strong> (m=undefined).<\/li>\n\n\n\n<li>A <strong>vertical line<\/strong> x=a parallel line will also be x=b (different constant).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-640afadf8e977733ec66d248b28ea942\" style=\"color:#000060\"><strong> Summary Table<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Type of Line<\/th><th>Slope Rule<\/th><th>Example<\/th><\/tr><\/thead><tbody><tr><td>Parallel<\/td><td>Same slope m<\/td><td>y=3x+2, y=3x\u22125<\/td><\/tr><tr><td>Perpendicular<\/td><td>m<sub>1<\/sub>\u00d7m<sub>2<\/sub>=\u22121<\/td><td>m<sub>1<\/sub>=4,m<sub>2<\/sub>=-1\/4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-0f342ac45fa25a567324a19ff2936acb\" style=\"color:#000060\"><strong> Practice Problems<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Write an equation of a line parallel to y=\u22123x+7 passing through (2, 5).<\/li>\n\n\n\n<li>Write an equation of a line perpendicular to y=5x\u22121 passing through (-4, 2).<\/li>\n\n\n\n<li>A line passes through (0, -3) and is parallel to y=2\/5x+4. Write its equation.<\/li>\n\n\n\n<li>Find the equation of a line perpendicular to y=\u22123\/4x+6 and passing through (1, 1).<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#9deec4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Line s has an equation of y = 3x + 4. Parallel to line s is line t, which passes<br>through the point (1, 6). <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-89a2916289f4fc10a48530755ac2cb99\" style=\"color:#b00012\">What is the equation of line t?<\/p>\n<\/div><\/div>\n\n\n\n<p>Step 1: Find the slope of line s.<\/p>\n\n\n\n<p>First, find the slope m of line s. This is the only time you will use the equation of line s.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y = \u20133x + 4<\/p>\n\n\n\n<p>Line s has a slope m of 3.<br><strong>Step 2: Find the slope of line t.<\/strong><br>Line t is parallel to s, so its slope is the same: -3.<br><strong>Step 3: Use the slope of line t and a point on line t to find its<br>y-intercept.<\/strong><br>Plug the slope m = 3 and the point (1, 6) into the slope-intercept formula.<br>Then solve for the y-intercept b.<br>y = mx + b<br>6 = 3(1) + b Plugin y = 6, m = 3, and x = 1<br>6 = 3 + b Multiply<br>9 = b Add 3 to both sides<br>Line t has a y-intercept of 9.<br>Step 4: Use the slope of line t and the y-intercept of line t to find the<br>equation of the line.<br>Plug the slope m =- 3 and the y-intercept b = 9 into the slope-intercept<br>formula.<br>y = mx + b<br>y = 3x + 9 Plugin m = -3 and b = 9<br>The equation of line t in slope-intercept form is y = -3x + 9<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ddb2f2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Line k has an equation of y = 2x + 7. Line l, which is perpendicular to line k,<br>includes the point (2, 7). <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-62247600abad63eef965f7176db48881\" style=\"color:#b00012\">What is the equation of line l?<\/p>\n<\/div><\/div>\n\n\n\n<p>Step 1: Find the slope of line k.<br>First, find the slope m of line k. This is the only time you will use the equation of line k.<br>y = mx + b<br>y = 2x + 7<br>Line k has a slope m of -2.<\/p>\n\n\n\n<p>Step 2: Find the slope of line l.<br>Line l is perpendicular to k, so its slope is the opposite reciprocal: 1\/2.<br>Step 3: Use the slope of line l and a point on line l to find its y-intercept.<\/p>\n\n\n\n<p>Step 3: Use the slope of line l and a point on line l to find its y-intercept.<\/p>\n\n\n\n<p>Plug the slope m=1\/2 and the point(2, \u20137) into the slope-intercept formula. Then solve for they-intercept b.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>\u20137 =1\/2 ( 2 )+b Plugin y= \u20137,m=1\/2, and x= 2<\/p>\n\n\n\n<p>\u20137 = 1 + b Multiply and simplify<\/p>\n\n\n\n<p>\u20138 = b     Subtract1 from both sides<\/p>\n\n\n\n<p>Line l has ay-intercept of\u20138.<\/p>\n\n\n\n<p>Step 4: Use the slope of line l and the y-intercept of line l to find the equation of the line.<\/p>\n\n\n\n<p>Plug the slope m=1\/2 and they-intercept b = \u20138 in to the slope-intercept formula.<\/p>\n\n\n\n<p>y = mx + b<\/p>\n\n\n\n<p>y =1\/2 x+\u20138 Plugin m=1\/2 and b= \u20138<\/p>\n\n\n\n<p>y =1\/2 x\u2212 8<br>Rewrite as subtraction<\/p>\n\n\n\n<p>The equation of line in slope-intercept form is y=1\/2 x\u2212 8<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#eb9c9c\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>The equation of line g is y =1\/7x \u2212 8. Line h includes the point (9, 1) and is parallel to line g. <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f32c4e95dbfc92e1c4c5f77916235285\" style=\"color:#b00012\">What is the equation of line h?<\/p>\n<\/div><\/div>\n\n\n\n<p>Step 1: Find the slope of line g.<br>First find the slope m of line g. This is the only time you will use the equation of<br>line g.<br>y = mx + b<br>y =1\/7x \u2212 8<br>Line g has a slope m of 1\/7.<\/p>\n\n\n\n<p>Step 2: Find the slope of line h.<br>Line h is parallel to g, so its slope is the same:1\/7.<br><\/p>\n\n\n\n<p>Step 3: Use the slope of line h and a point on line h to find its<br>y-intercept. Plug the slope m =1\/7 and the point (9, 1) into the slope-intercept formula.<br>Then solve for the y-intercept b.<br>y = mx + b<br>1 =1\/7(9) + b Plug in y = 1, m =1\/7, and x = 9<br>1 =9\/7+b Multiply = b Subtract 9\/7 from both sides = b Rewrite with a common denominator<br>= b Subtract Line h has a y-intercept of -2\/7.<br>Step 4: Use the slope of line h and the y-intercept of line h to find the<br>equation of the line.<br>Plug the slope m =1\/7and the y-intercept b =-2\/7 into the slope-intercept<br>formula.<br>y = mx + b<br>y =1\/7x +-2\/7 Plug in m =1\/7 and b =-2\/7<br>y =1\/7x \u22122\/7 Rewrite as subtraction<\/p>\n\n\n\n<p><br>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#ffef76\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-28.png\" alt=\"\" class=\"wp-image-9311\"\/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/169572335859113fhf1q-voicemaker.in-speech.mp3\"><\/audio><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e9969cedcddfdc22a0f1cf481aeb5cd5\" style=\"color:#d90000\">Let&#8217;s practice:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78334\/885\/861\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-125.png\" alt=\"\" class=\"wp-image-8076\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-125.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-125-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-125-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78344\/611\/491\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-134.png\" alt=\"\" class=\"wp-image-8077\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-134.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-134-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-134-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#b42d2d\"><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Write an equation for a parallel or perpendicular line T.20 Write an equation for a parallel or perpendicular\u00a0line by Delta publications key notes: Recap: Slope-Intercept Form A line in slope-intercept form is: y=mx+b where: Parallel Lines Steps to write the equation: y\u2212y1=m(x\u2212x1) Simplify to slope-intercept form y=mx+b Example:Write an equation of a line parallel to<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-20-write-an-equation-for-a-parallel-or-perpendicular-line\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.20 Write an equation for a parallel or perpendicular line&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-337","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=337"}],"version-history":[{"count":26,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/337\/revisions"}],"predecessor-version":[{"id":17565,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/337\/revisions\/17565"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}