{"id":345,"date":"2015-09-18T22:40:16","date_gmt":"2015-09-18T22:40:16","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=345"},"modified":"2015-11-04T22:32:20","modified_gmt":"2015-11-04T22:32:20","slug":"finding-x-intercepts-and-y-intercepts","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/finding-x-intercepts-and-y-intercepts\/","title":{"raw":"Finding x-intercepts and y-intercepts","rendered":"Finding x-intercepts and y-intercepts"},"content":{"raw":"The intercepts<\/strong> of a graph are points at which the graph crosses the axes. The x-<\/em>intercept<\/strong> is the point at which the graph crosses the x-<\/em>axis. At this point, the y-<\/em>coordinate is zero. The y-<\/em>intercept<\/strong> is the point at which the graph crosses the y-<\/em>axis. At this point, the x-<\/em>coordinate is zero.\r\n\r\nTo determine the x-<\/em>intercept, we set y <\/em>equal to zero and solve for x<\/em>. Similarly, to determine the y-<\/em>intercept, we set x <\/em>equal to zero and solve for y<\/em>. For example, lets find the intercepts of the equation [latex]y=3x - 1[\/latex].\r\n\r\nTo find the x-<\/em>intercept, set [latex]y=0[\/latex].\r\n
[latex]\\begin{array}{ll}y=3x - 1\\hfill & \\hfill \\\\ 0=3x - 1\\hfill & \\hfill \\\\ 1=3x\\hfill & \\hfill \\\\ \\frac{1}{3}=x\\hfill & \\hfill \\\\ \\left(\\frac{1}{3},0\\right)\\hfill & x\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\r\nTo find the y-<\/em>intercept, set [latex]x=0[\/latex].\r\n
[latex]\\begin{array}{l}y=3x - 1\\hfill \\\\ y=3\\left(0\\right)-1\\hfill \\\\ y=-1\\hfill \\\\ \\left(0,-1\\right)y\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\r\nWe can confirm that our results make sense by observing a graph of the equation as in Figure 10. Notice that the graph crosses the axes where we predicted it would.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"This Figure 12<\/b>[\/caption]\r\n\r\n
\r\n

How To: Given an equation, find the intercepts.<\/h3>\r\n
    \r\n\t
  1. Find the x<\/em>-intercept by setting [latex]y=0[\/latex] and solving for [latex]x[\/latex].<\/li>\r\n\t
  2. Find the y-<\/em>intercept by setting [latex]x=0[\/latex] and solving for [latex]y[\/latex].<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Example 4: Finding the Intercepts of the Given Equation<\/h3>\r\nFind the intercepts of the equation [latex]y=-3x - 4[\/latex]. Then sketch the graph using only the intercepts.\r\n\r\n<\/div>\r\n
    \r\n

    Solution<\/h3>\r\nSet [latex]y=0[\/latex] to find the x-<\/em>intercept.\r\n
    [latex]\\begin{array}{l}y=-3x - 4\\hfill \\\\ 0=-3x - 4\\hfill \\\\ 4=-3x\\hfill \\\\ -\\frac{4}{3}=x\\hfill \\\\ \\left(-\\frac{4}{3},0\\right)x\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\r\nSet [latex]x=0[\/latex] to find the y-<\/em>intercept.\r\n
    [latex]\\begin{array}{l}y=-3x - 4\\hfill \\\\ y=-3\\left(0\\right)-4\\hfill \\\\ y=-4\\hfill \\\\ \\left(0,-4\\right)y\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\r\nPlot both points, and draw a line passing through them as in Figure 11.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"This Figure 13<\/b>[\/caption]\r\n\r\n<\/div>\r\n
    \r\n

    Try It 1<\/h3>\r\nFind the intercepts of the equation and sketch the graph: [latex]y=-\\frac{3}{4}x+3[\/latex].\r\n\r\nSolution<\/a>\r\n\r\n<\/div>\r\n ","rendered":"

    The intercepts<\/strong> of a graph are points at which the graph crosses the axes. The x-<\/em>intercept<\/strong> is the point at which the graph crosses the x-<\/em>axis. At this point, the y-<\/em>coordinate is zero. The y-<\/em>intercept<\/strong> is the point at which the graph crosses the y-<\/em>axis. At this point, the x-<\/em>coordinate is zero.<\/p>\n

    To determine the x-<\/em>intercept, we set y <\/em>equal to zero and solve for x<\/em>. Similarly, to determine the y-<\/em>intercept, we set x <\/em>equal to zero and solve for y<\/em>. For example, lets find the intercepts of the equation [latex]y=3x - 1[\/latex].<\/p>\n

    To find the x-<\/em>intercept, set [latex]y=0[\/latex].<\/p>\n

    [latex]\\begin{array}{ll}y=3x - 1\\hfill & \\hfill \\\\ 0=3x - 1\\hfill & \\hfill \\\\ 1=3x\\hfill & \\hfill \\\\ \\frac{1}{3}=x\\hfill & \\hfill \\\\ \\left(\\frac{1}{3},0\\right)\\hfill & x\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\n

    To find the y-<\/em>intercept, set [latex]x=0[\/latex].<\/p>\n

    [latex]\\begin{array}{l}y=3x - 1\\hfill \\\\ y=3\\left(0\\right)-1\\hfill \\\\ y=-1\\hfill \\\\ \\left(0,-1\\right)y\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\n

    We can confirm that our results make sense by observing a graph of the equation as in Figure 10. Notice that the graph crosses the axes where we predicted it would.<\/p>\n

    \"This<\/p>\n

    Figure 12<\/b><\/p>\n<\/div>\n

    \n

    How To: Given an equation, find the intercepts.<\/h3>\n
      \n
    1. Find the x<\/em>-intercept by setting [latex]y=0[\/latex] and solving for [latex]x[\/latex].<\/li>\n
    2. Find the y-<\/em>intercept by setting [latex]x=0[\/latex] and solving for [latex]y[\/latex].<\/li>\n<\/ol>\n<\/div>\n
      \n

      Example 4: Finding the Intercepts of the Given Equation<\/h3>\n

      Find the intercepts of the equation [latex]y=-3x - 4[\/latex]. Then sketch the graph using only the intercepts.<\/p>\n<\/div>\n

      \n

      Solution<\/h3>\n

      Set [latex]y=0[\/latex] to find the x-<\/em>intercept.<\/p>\n

      [latex]\\begin{array}{l}y=-3x - 4\\hfill \\\\ 0=-3x - 4\\hfill \\\\ 4=-3x\\hfill \\\\ -\\frac{4}{3}=x\\hfill \\\\ \\left(-\\frac{4}{3},0\\right)x\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\n

      Set [latex]x=0[\/latex] to find the y-<\/em>intercept.<\/p>\n

      [latex]\\begin{array}{l}y=-3x - 4\\hfill \\\\ y=-3\\left(0\\right)-4\\hfill \\\\ y=-4\\hfill \\\\ \\left(0,-4\\right)y\\text{-intercept}\\hfill \\end{array}[\/latex]<\/div>\n

      Plot both points, and draw a line passing through them as in Figure 11.<\/p>\n

      \"This<\/p>\n

      Figure 13<\/b><\/p>\n<\/div>\n<\/div>\n

      \n

      Try It 1<\/h3>\n

      Find the intercepts of the equation and sketch the graph: [latex]y=-\\frac{3}{4}x+3[\/latex].<\/p>\n

      Solution<\/a><\/p>\n<\/div>\n

       <\/p>\n\n\t\t\t

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