{"id":6058,"date":"2021-10-04T23:51:52","date_gmt":"2021-10-04T18:21:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6058"},"modified":"2021-10-04T23:52:12","modified_gmt":"2021-10-04T18:22:12","slug":"straight-line-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/straight-line-examples\/","title":{"rendered":"Straight Line Examples"},"content":{"rendered":"

Here you will learn some straight line examples for better understanding of straight line concepts<\/a><\/span>.<\/p>\n\n\n

\n
\n\n \n

Example 1 : <\/span>Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14.<\/p>\n

Solution : <\/span>Let the equation of line be \\(x\\over a\\) + \\(y\\over b\\) = 1   …..(i)

\n This line passes through (3,4), therefore \\(3\\over a\\) + \\(4\\over b\\) = 1   …….(ii)

\n It is given that a + b = 14   \\(\\implies\\)   b = 14 – a in (ii), we get

\n \\(3\\over a\\) + \\(4\\over 14 – a\\) = 1   \\(\\implies\\)   \\(a^2\\) – 13a + 42 = 0

\n \\(\\implies\\)   (a – 7)(a – 6) = 0   \\(\\implies\\)   a = 7, 6

\n for a = 7, b = 14 – 7 = 7 and for a = 6, b = 14 – 6 = 8

\n Putting the values of a and b in (i), we get the equations of lines

\n \\(x\\over 7\\) + \\(y\\over 7\\) = 1   and   \\(x\\over 6\\) + \\(y\\over 8\\) = 1<\/p>\n


\n\n \n

Example 2 : <\/span> If x + 4y – 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k is – <\/p>\n

Solution : <\/span> \\(m_1\\) = -\\(1\\over 4\\)   \\(m_2\\) = -\\(4\\over k\\)

\n Two lines are perpendicular if \\(m_1 m_2\\) = -1

\n \\(\\implies\\)   (-\\(1\\over 4\\))\\(\\times\\)(-\\(4\\over k\\)) = -1   \\(\\implies\\)   k = -1\n <\/p>


\n\n \n

Example 3 : <\/span> If the straight line 3x + 4y + 5 – k(x + y + 3) = 0 is parallel to y-axis, then the value of k is –<\/p>\n

Solution : <\/span>A straight line is parallel to y-axis, if its y-coefficient is zero

\n i.e. 4 – k = 0   i.e.   k = 4<\/p>\n


\n\n \n

Example 4 : <\/span> If \\(\\lambda x^2 – 10xy + 12y^2 + 5x – 16y – 3\\) = 0 represents a pair of straight lines, then \\(\\lambda\\) is equal to –<\/p>\n

Solution : <\/span>Comparing with \\(ax^2+2hxy+by^2+2gx+2fy+c\\) = 0

\n Here a = \\(\\lambda\\), b = 12, c = -3, f = -8, g = 5\/2, h = -5

\n Using condition \\(abc+2fgh-af^2-bg^2-ch^2\\) = 0, we have

\n \\(\\lambda\\)(12)(-3) + 2(-8)(5\/2)(-5) – \\(\\lambda\\)(64) – 12(25\/4) + 3(25) = 0

\n \\(\\implies\\)   -36\\(\\lambda\\) + 200 – 64\\(\\lambda\\) – 75 + 75 = 0

\n \\(\\implies\\)   100\\(\\lambda\\) = 200

\n \\(\\therefore\\)   \\(\\lambda\\) = 2<\/p>\n
\n

Practice these given straight line examples to test your knowledge on concepts of straight lines.<\/p>\n \n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some straight line examples for better understanding of straight line concepts. Example 1 : Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14. Solution : Let the equation of line be \\(x\\over a\\) + \\(y\\over b\\) = 1   …<\/p>\n

Straight Line Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[32],"tags":[],"yoast_head":"\nStraight Line Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these straight line examples to practice and test your knowledge of straight line concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/straight-line-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Straight Line Examples - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solve these straight line examples to practice and test your knowledge of straight line concepts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/straight-line-examples\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-04T18:21:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-04T18:22:12+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Straight Line Examples\",\"datePublished\":\"2021-10-04T18:21:52+00:00\",\"dateModified\":\"2021-10-04T18:22:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/\"},\"wordCount\":313,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Straight Line\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/straight-line-examples\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/\",\"url\":\"https:\/\/mathemerize.com\/straight-line-examples\/\",\"name\":\"Straight Line Examples - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-04T18:21:52+00:00\",\"dateModified\":\"2021-10-04T18:22:12+00:00\",\"description\":\"Solve these straight line examples to practice and test your knowledge of straight line concepts.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/straight-line-examples\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/straight-line-examples\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Straight Line Examples\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Straight Line Examples - Mathemerize","description":"Solve these straight line examples to practice and test your knowledge of straight line concepts.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/straight-line-examples\/","og_locale":"en_US","og_type":"article","og_title":"Straight Line Examples - Mathemerize","og_description":"Solve these straight line examples to practice and test your knowledge of straight line concepts.","og_url":"https:\/\/mathemerize.com\/straight-line-examples\/","og_site_name":"Mathemerize","article_published_time":"2021-10-04T18:21:52+00:00","article_modified_time":"2021-10-04T18:22:12+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/straight-line-examples\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/straight-line-examples\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Straight Line Examples","datePublished":"2021-10-04T18:21:52+00:00","dateModified":"2021-10-04T18:22:12+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/straight-line-examples\/"},"wordCount":313,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Straight Line"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/straight-line-examples\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/straight-line-examples\/","url":"https:\/\/mathemerize.com\/straight-line-examples\/","name":"Straight Line Examples - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-04T18:21:52+00:00","dateModified":"2021-10-04T18:22:12+00:00","description":"Solve these straight line examples to practice and test your knowledge of straight line concepts.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/straight-line-examples\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/straight-line-examples\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/straight-line-examples\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Straight Line Examples"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6058"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=6058"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6058\/revisions"}],"predecessor-version":[{"id":6061,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6058\/revisions\/6061"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=6058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=6058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=6058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}