{"id":231056,"date":"2025-06-10T11:56:55","date_gmt":"2025-06-10T11:56:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231056"},"modified":"2025-06-10T11:56:56","modified_gmt":"2025-06-10T11:56:56","slug":"find-the-slope-of-a-line-parallel-to-3x-4y-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/10\/find-the-slope-of-a-line-parallel-to-3x-4y-12\/","title":{"rendered":"Find the slope of a line parallel to 3x – 4y = 12."},"content":{"rendered":"\n

Find the slope of a line parallel to 3x – 4y = 12.<\/p>\n\n\n\n

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

Step 1: Convert to slope-intercept form<\/h3>\n\n\n\n

Starting with the given equation:<\/p>\n\n\n\n

3x\u22124y=123x – 4y = 12<\/p>\n\n\n\n

Solve for y<\/em>:<\/p>\n\n\n\n

    \n
  1. Subtract 3x<\/strong> from both sides:<\/li>\n<\/ol>\n\n\n\n

    \u22124y=\u22123x+12-4y = -3x + 12<\/p>\n\n\n\n

      \n
    1. Divide by -4<\/strong>:<\/li>\n<\/ol>\n\n\n\n

      y=34x\u22123y = \\frac{3}{4}x – 3<\/p>\n\n\n\n

      Now, we can see that the slope m<\/strong> is 3\/4<\/strong>.<\/p>\n\n\n\n

      Step 2: Parallel lines have the same slope<\/h3>\n\n\n\n

      A line parallel to 3x – 4y = 12<\/strong> will have the same<\/strong> slope. Thus, the slope of the parallel line is 3\/4<\/strong>.<\/p>\n\n\n\n

      Explanation <\/h3>\n\n\n\n

      The concept of parallel lines in mathematics follows a simple principle: if two lines are parallel, they have identical slopes. This ensures that they maintain a constant separation and never intersect, no matter how far they are extended.<\/p>\n\n\n\n

      In the given equation, 3x – 4y = 12<\/strong>, we first convert it into the slope-intercept form y = mx + b<\/strong>. This transformation helps us clearly identify the slope of the line, represented by m<\/em>. By isolating y<\/em>, we determine that m = 3\/4<\/em>.<\/p>\n\n\n\n

      Since the defining characteristic of parallel lines is having identical slopes, any line parallel to 3x – 4y = 12<\/strong> must share the same slope of 3\/4<\/strong>. This rule is derived from the equation of a straight line and ensures that no matter what the y-intercept is, the two lines remain equidistant.<\/p>\n\n\n\n

      Understanding this principle is crucial in geometry and algebra, especially in applications like designing roads, constructing buildings, and even physics simulations, where maintaining parallel structures is necessary. The concept extends beyond simple equations into real-world problems, where engineers, architects, and planners rely on parallelism to ensure stability and functionality.<\/p>\n\n\n\n

      So, the final answer is 3\/4<\/strong>.<\/p>\n\n\n\n

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

      Find the slope of a line parallel to 3x – 4y = 12. The correct Answer and Explanation is: Step 1: Convert to slope-intercept form Starting with the given equation: 3x\u22124y=123x – 4y = 12 Solve for y: \u22124y=\u22123x+12-4y = -3x + 12 y=34x\u22123y = \\frac{3}{4}x – 3 Now, we can see that the slope […]<\/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-231056","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231056","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=231056"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231056\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231056"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231056"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}