{"id":150350,"date":"2024-10-08T17:07:34","date_gmt":"2024-10-08T17:07:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=150350"},"modified":"2024-10-08T17:07:37","modified_gmt":"2024-10-08T17:07:37","slug":"a-line-has-a-slope-of-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/08\/a-line-has-a-slope-of-4\/","title":{"rendered":"A line has a slope of 4"},"content":{"rendered":"\n<p>A line has a slope of 4. What is the slope of any line perpendicular to this line? A \u22124 B \u221214 C 14 D undefined<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong> (-\\frac{1}{4})<\/strong><\/mark><\/p>\n\n\n\n<p>To find the slope of a line that is perpendicular to another line, we use the property that the product of the slopes of two perpendicular lines is (-1). This means if one line has a slope (m_1) and another line has a slope (m_2), then:<\/p>\n\n\n\n<p>[ m_1 \\times m_2 = -1 ]<\/p>\n\n\n\n<p>Given that the slope of the first line is (m_1 = 4), we can set up the equation to find (m_2), the slope of the line perpendicular to it:<\/p>\n\n\n\n<p>[ 4 \\times m_2 = -1 ]<\/p>\n\n\n\n<p>To isolate (m_2), we divide both sides of the equation by (4):<\/p>\n\n\n\n<p>[ m_2 = \\frac{-1}{4} ]<\/p>\n\n\n\n<p>Thus, the slope of the line that is perpendicular to the original line with a slope of (4) is (-\\frac{1}{4}).<\/p>\n\n\n\n<p>However, let&#8217;s analyze the provided answer choices:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A<\/strong>: (-4)<\/li>\n\n\n\n<li><strong>B<\/strong>: (-14)<\/li>\n\n\n\n<li><strong>C<\/strong>: (14)<\/li>\n\n\n\n<li><strong>D<\/strong>: undefined<\/li>\n<\/ul>\n\n\n\n<p>None of these options match (-\\frac{1}{4}). It is possible that there was a misunderstanding in the question or the answer choices provided. The correct slope for any line perpendicular to a line with a slope of (4) is indeed (-\\frac{1}{4}).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary<\/h3>\n\n\n\n<p>In summary, the slope of a line that is perpendicular to another line with a slope of (4) is (-\\frac{1}{4}). The concept of perpendicular slopes is fundamental in geometry and algebra. Remembering that the product of the slopes must equal (-1) allows you to quickly calculate perpendicular slopes, making it a useful tool in various mathematical applications, including analytic geometry, calculus, and more advanced topics in mathematics. Understanding this relationship deepens comprehension of the behavior of lines in a coordinate plane.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A line has a slope of 4. What is the slope of any line perpendicular to this line? A \u22124 B \u221214 C 14 D undefined The Correct Answer and Explanation is : The correct answer is: (-\\frac{1}{4}) To find the slope of a line that is perpendicular to another line, we use the property [&hellip;]<\/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-150350","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150350","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=150350"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/150350\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=150350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=150350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=150350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}