{"id":191677,"date":"2025-02-15T10:02:50","date_gmt":"2025-02-15T10:02:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191677"},"modified":"2025-02-15T10:02:52","modified_gmt":"2025-02-15T10:02:52","slug":"rewrite-in-slope-intercept-form-6x-2y-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/15\/rewrite-in-slope-intercept-form-6x-2y-12\/","title":{"rendered":"Rewrite in slope-intercept form: 6x + 2y = 12"},"content":{"rendered":"\n

Rewrite in slope-intercept form: 6x + 2y = 12<\/p>\n\n\n\n

A. y = -3x + 6<\/p>\n\n\n\n

B. y = 3x +12<\/p>\n\n\n\n

C. y = 3x – 6<\/p>\n\n\n\n

D. y = 6x \u2013 12<\/p>\n\n\n\n

E. None<\/p>\n\n\n\n

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

To rewrite the equation (6x + 2y = 12) in slope-intercept form, we need to solve for (y).<\/p>\n\n\n\n

Step-by-Step Process:<\/h3>\n\n\n\n
    \n
  1. Start with the given equation:<\/strong>
    [
    6x + 2y = 12
    ]<\/li>\n\n\n\n
  2. Isolate the (y)-term:<\/strong>
    Subtract (6x) from both sides to move the (x)-term to the right-hand side:
    [
    2y = -6x + 12
    ]<\/li>\n\n\n\n
  3. Solve for (y):<\/strong>
    Divide both sides of the equation by 2 to get (y) by itself:
    [
    y = \\frac{-6x + 12}{2}
    ]
    Simplify the terms:
    [
    y = -3x + 6
    ]<\/li>\n<\/ol>\n\n\n\n

    Thus, the equation in slope-intercept form is:
    [
    y = -3x + 6
    ]<\/p>\n\n\n\n

    Slope-Intercept Form:<\/h3>\n\n\n\n

    The slope-intercept form of an equation is written as (y = mx + b), where:<\/p>\n\n\n\n

      \n
    • (m) is the slope of the line.<\/li>\n\n\n\n
    • (b) is the y-intercept, the point where the line crosses the y-axis.<\/li>\n<\/ul>\n\n\n\n

      In the equation (y = -3x + 6):<\/p>\n\n\n\n

        \n
      • The slope (m = -3), meaning that for every unit increase in (x), (y) decreases by 3 units.<\/li>\n\n\n\n
      • The y-intercept (b = 6), meaning the line crosses the y-axis at (y = 6).<\/li>\n<\/ul>\n\n\n\n

        Answer:<\/h3>\n\n\n\n

        The correct answer is:
        A. y = -3x + 6<\/strong><\/p>\n\n\n\n

        I will now generate an image to visually show the slope-intercept form equation.<\/p>\n\n\n\n

        Here is the graph that represents the equation (y = -3x + 6). It shows how the line behaves, crossing the y-axis at 6 and having a slope of -3. This visual should help you understand the relationship between the equation and the graph! Let me know if you need further explanation or another visual.<\/p>\n\n\n\n

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

        Rewrite in slope-intercept form: 6x + 2y = 12 A. y = -3x + 6 B. y = 3x +12 C. y = 3x – 6 D. y = 6x \u2013 12 E. None The Correct Answer and Explanation is : To rewrite the equation (6x + 2y = 12) in slope-intercept form, we need […]<\/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-191677","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191677","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=191677"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191677\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}