{"id":242461,"date":"2025-07-04T07:40:40","date_gmt":"2025-07-04T07:40:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242461"},"modified":"2025-07-04T07:40:42","modified_gmt":"2025-07-04T07:40:42","slug":"identify-the-slope-y-intercept","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/identify-the-slope-y-intercept\/","title":{"rendered":"Identify the SLOPE & Y-INTERCEPT."},"content":{"rendered":"\n

Identify the SLOPE & Y-INTERCEPT. Then graph. x – 3y = 9<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Correct Answer:<\/strong>
Slope (m):<\/strong> 1\/3
Y-Intercept (b):<\/strong> -3, or the point (0, -3)<\/p>\n\n\n\n

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

To identify the slope and y-intercept of the linear equation x – 3y = 9, the most effective method is to convert it into slope-intercept form, which is written as y = mx + b<\/strong>. In this format, ‘m’ represents the slope of the line, and ‘b’ represents the y-intercept, which is the point where the line crosses the vertical y-axis.<\/p>\n\n\n\n

Step 1: Convert the Equation to Slope-Intercept Form (y = mx + b)<\/strong><\/p>\n\n\n\n

    \n
  1. Start with the given equation:
    x – 3y = 9<\/li>\n\n\n\n
  2. The goal is to isolate the ‘y’ variable on one side of the equation. First, move the ‘x’ term to the other side by subtracting ‘x’ from both sides:
    x – x – 3y = 9 – x
    -3y = -x + 9<\/li>\n\n\n\n
  3. Now, solve for ‘y’ by dividing every term in the equation by -3. This will get ‘y’ by itself:
    (-3y) \/ -3 = (-x) \/ -3 + (9) \/ -3<\/li>\n\n\n\n
  4. Simplify each term:
    y = (1\/3)x – 3<\/li>\n<\/ol>\n\n\n\n

    Step 2: Identify the Slope and Y-Intercept<\/strong><\/p>\n\n\n\n

    Now that the equation is in the y = mx + b format, we can directly identify the components:<\/p>\n\n\n\n

      \n
    • The\u00a0slope (m)<\/strong>\u00a0is the coefficient of the ‘x’ term, which is\u00a01\/3<\/strong>. A slope of 1\/3 means for every 3 units you move to the right on the graph (the “run”), you move 1 unit up (the “rise”).<\/li>\n\n\n\n
    • The\u00a0y-intercept (b)<\/strong>\u00a0is the constant term, which is\u00a0-3<\/strong>. This means the line crosses the y-axis at the point\u00a0(0, -3)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Step 3: Graph the Line<\/strong><\/p>\n\n\n\n

        \n
      1. Plot the y-intercept:<\/strong>\u00a0Begin by placing a point on the y-axis at -3. This is the point (0, -3).<\/li>\n\n\n\n
      2. Use the slope to find a second point:<\/strong>\u00a0The slope is 1\/3 (rise\/run). Starting from your first point at (0, -3), “rise” 1 unit up and “run” 3 units to the right.\n
          \n
        • From (0, -3), move up 1 unit to (0, -2).<\/li>\n\n\n\n
        • From (0, -2), move right 3 units to (3, -2).<\/li>\n\n\n\n
        • This gives you a second point on the line at\u00a0(3, -2)<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Draw the line:<\/strong>\u00a0Connect the two points, (0, -3) and (3, -2), with a straight line. Extend this line in both directions with arrows to show it continues infinitely.<\/li>\n<\/ol>\n\n\n\n

          This process provides a clear visual representation of the equation x – 3y = 9.<\/p>\n\n\n\n

          (A graph would be drawn here showing a line passing through the points (0, -3) and (3, -2).)<\/strong><\/p>\n\n\n\n

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

          Identify the SLOPE & Y-INTERCEPT. Then graph. x – 3y = 9 The Correct Answer and Explanation is: Correct Answer:Slope (m): 1\/3Y-Intercept (b): -3, or the point (0, -3) Explanation: To identify the slope and y-intercept of the linear equation x – 3y = 9, the most effective method is to convert it into slope-intercept form, which is […]<\/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-242461","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242461","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=242461"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242461\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}