{"id":261218,"date":"2025-07-19T21:54:39","date_gmt":"2025-07-19T21:54:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=261218"},"modified":"2025-07-19T21:54:41","modified_gmt":"2025-07-19T21:54:41","slug":"write-4x-3y-6-in-the-form-y-mx-b","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/write-4x-3y-6-in-the-form-y-mx-b\/","title":{"rendered":"Write 4x + 3y = 6 in the form y = mx + b."},"content":{"rendered":"\n

Write 4x + 3y = 6 in the form y = mx + b.<\/p>\n\n\n\n

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

To rewrite the equation 4x+3y=64x + 3y = 64x+3y=6 in the form y=mx+by = mx + by=mx+b, which is the slope-intercept form of a linear equation, we need to isolate yyy on one side of the equation.<\/p>\n\n\n\n

Here are the steps to do that:<\/p>\n\n\n\n

    \n
  1. Start with the given equation: 4x+3y=64x + 3y = 64x+3y=6<\/li>\n\n\n\n
  2. Subtract 4x4x4x from both sides to get rid of the 4x4x4x term on the left: 3y=\u22124x+63y = -4x + 63y=\u22124x+6<\/li>\n\n\n\n
  3. Now, to isolate yyy, divide both sides of the equation by 3: y=\u22124x+63y = \\frac{-4x + 6}{3}y=3\u22124x+6\u200b<\/li>\n\n\n\n
  4. Simplify the right side by dividing both terms: y=\u221243x+2y = -\\frac{4}{3}x + 2y=\u221234\u200bx+2<\/li>\n<\/ol>\n\n\n\n

    So the equation in the slope-intercept form is: y=\u221243x+2y = -\\frac{4}{3}x + 2y=\u221234\u200bx+2<\/p>\n\n\n\n

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

    The equation y=mx+by = mx + by=mx+b is called the slope-intercept form of a linear equation. In this form:<\/p>\n\n\n\n

      \n
    • mmm represents the slope of the line.<\/li>\n\n\n\n
    • bbb represents the y-intercept, which is the point where the line crosses the y-axis.<\/li>\n<\/ul>\n\n\n\n

      In the equation y=\u221243x+2y = -\\frac{4}{3}x + 2y=\u221234\u200bx+2:<\/p>\n\n\n\n

        \n
      • The slope m=\u221243m = -\\frac{4}{3}m=\u221234\u200b, which tells you that for every 3 units you move horizontally to the right along the x-axis, the line moves down 4 units. This gives the line a negative slope, meaning it goes downhill from left to right.<\/li>\n\n\n\n
      • The y-intercept b=2b = 2b=2, meaning the line crosses the y-axis at the point (0, 2).<\/li>\n<\/ul>\n\n\n\n

        This process is a common way of rearranging a linear equation to better understand the relationship between the variables and visualize it on a graph.<\/p>\n\n\n\n

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

        Write 4x + 3y = 6 in the form y = mx + b. The Correct Answer and Explanation is: To rewrite the equation 4x+3y=64x + 3y = 64x+3y=6 in the form y=mx+by = mx + by=mx+b, which is the slope-intercept form of a linear equation, we need to isolate yyy on one side of […]<\/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-261218","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261218","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=261218"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261218\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}