{"id":247891,"date":"2025-07-07T20:31:55","date_gmt":"2025-07-07T20:31:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=247891"},"modified":"2025-07-07T20:31:57","modified_gmt":"2025-07-07T20:31:57","slug":"write-an-equation-in-standard-form-of-the-line-passing-through-67-with-an-undefined-slope","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/write-an-equation-in-standard-form-of-the-line-passing-through-67-with-an-undefined-slope\/","title":{"rendered":"Write an equation in standard form of the line passing through (6,7) with an undefined slope"},"content":{"rendered":"\n

Write an equation in standard form of the line passing through (6,7) with an undefined slope. The standard form of the equation of the line passing through (6,7) with an undefined slope is given by (Simplify your answer.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The equation of a line with an undefined slope is a vertical line<\/strong>. Vertical lines have the general form:x=constantx = \\text{constant}x=constant<\/p>\n\n\n\n

For a line passing through the point (6,7)(6,7)(6,7), the constant is the x-coordinate<\/strong> of the point, which is 6. Therefore, the equation of the line is:x=6x = 6x=6<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n
    \n
  1. Slope and Undefined Slope<\/strong>:\n
      \n
    • The slope of a line represents the rate of change<\/strong> of the y-coordinate with respect to the x-coordinate. For most lines, the slope is a finite number.<\/li>\n\n\n\n
    • A line with an undefined slope<\/strong> means that there is no change in x<\/strong> while y changes. This happens for vertical lines, where all points on the line have the same x-coordinate. As you move up or down the line, the x-value does not change.<\/li>\n\n\n\n
    • This is why the equation of a vertical line is simply x=constantx = \\text{constant}x=constant.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Standard Form of a Line<\/strong>:\n
        \n
      • The standard form of a linear equation is generally written as Ax+By=CAx + By = CAx+By=C, where AAA, BBB, and CCC are constants, and AAA and BBB are not both zero.<\/li>\n\n\n\n
      • For vertical lines, the equation does not involve yyy at all. So, it cannot be written in the form Ax+By=CAx + By = CAx+By=C (because it doesn’t have a yyy-term), but it can be represented as x=constantx = \\text{constant}x=constant.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

        Thus, the equation of the vertical line passing through the point (6,7)(6,7)(6,7) is:x=6x = 6x=6<\/p>\n\n\n\n

        This line has an undefined slope<\/strong>, and it is a vertical line because all points on it will have an x-coordinate of 6, no matter the value of yyy.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Write an equation in standard form of the line passing through (6,7) with an undefined slope. The standard form of the equation of the line passing through (6,7) with an undefined slope is given by (Simplify your answer. The Correct Answer and Explanation is: The equation of a line with an undefined slope is a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-247891","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=247891"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247891\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=247891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=247891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=247891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}