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<h4>Finding Intercepts from Graphs and Equations</h4>

      <p>The points where a line crosses the \( x \)-axis and the \( y \)-axis are called the intercepts of the line.</p>
   
      <p>Let&rsquo;s look at the graphs of the lines.</p>
   
    <img alt="The figure shows four graphs of different equations. In example a the graph of 2 x plus y plus 6 is graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The points (0, 6) and (3, 0) are plotted and labeled. A straight line goes through both points and has arrows on both ends. In example b the graph of 3 x minus 4 y plus 12 is graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The points (0, negative 3) and (4, 0) are plotted and labeled. A straight line goes through both points and has arrows on both ends. In example c the graph of x minus y plus 5 is graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The points (0, negative 5) and (5, 0) are plotted and labeled. A straight line goes through both points and has arrows on both ends. In example d the graph of y plus negative 2 x is graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The point (0, 0) is plotted and labeled. A straight line goes through this point and the points (negative 1, 2) and (1, negative 2) and has arrows on both ends." class="img-fluid atto_image_button_text-bottom" height="716" src="https://k12.openstax.org/contents/raise/resources/fe7c894af22fc816272cc2a3a72e056a1da78b83" width="643">

  <br>
    <br>
  <p>First, notice where each of these lines crosses the <em>\( x \)</em>-axis.</p>
  <p>Now, let&rsquo;s look at the points where these lines cross the <em>\( y \)</em>-axis.</p>
  <table class="os-raise-wideequaltable">
  <thead>
    <tr>
      <th scope="col">Figure</th>
      <th scope="col">The Line Crosses the \(x\)-axis at:</th>
      <th scope="col">Ordered Pair for this Point</th>
      <th scope="col">The Line Crosses the \(y\)-axis at:</th>
      <th scope="col">Ordered Pair for this Point</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Figure (a)</td>
      <td>3</td>
      <td>\((3,0)\)</td>
      <td>6</td>
      <td>\((0,6)\)</td>
    </tr>
    <tr>
      <td>Figure (b)</td>
      <td>4</td>
      <td>\((4,0)\)</td>
      <td>-3</td>
      <td>\((0,-3)\)</td>
    </tr>
    <tr>
      <td>Figure (c)</td>
      <td>5</td>
      <td>\((5,0)\)</td>
      <td>-5</td>
      <td>\((0,5)\)</td>
    </tr>
    <tr>
      <td>Figure (d)</td>
      <td>0</td>
      <td>\((0,0)\)</td>
      <td>0</td>
      <td>\((0,0)\)</td>
    </tr>
    <tr>
      <td>General Figure</td>
      <td>\(a\)</td>
      <td>(\(a,0)\)</td>
      <td>\(b\)</td>
      <td>(0,\(b)\)</td>
    </tr>
  </tbody>
</table>
  <br>
  <p class="os-raise-text-bold">\(X\)-INTERCEPT and \(Y\)-INTERCEPT of a Line</p>
<p> The  \(x\) -intercept is the point  \( (a , 0) \) where the line crosses the  \(x\)-axis. <br>
  The  \(y\)-intercept is the point \( (0 , b) \) where the line crosses the \(y\)-axis.</p>
<img
        alt="The table has 3 rows and 2 columns. The first row is a header row with the headers x and y. The second row contains a and 0. The third row contains 0 and b."
        class="img-fluid atto_image_button_text-bottom" height="92"
        src="https://k12.openstax.org/contents/raise/resources/cfa22a98c89816890def2a20a309f5e74ebe366d"
        width="429"><br>
<br>
<p class="os-raise-text-bold">Find the \( x \)- and \( y \)-intercepts from the Equation of a Line</p>
<p> Use the equation of the line. To find: </p>
<ul>
  <li> the \(x\)-intercept of the line, let \( y = 0 \) and solve for \( x \). </li>
  <li> the \(y\)-intercept of the line, let \( x = 0 \) and solve for \( y \). </li>
</ul>
<p class="os-raise-text-bold">Example</p>
<p>Find the intercepts of \( 2x + y = 8 \)</p>
       <p class="os-raise-text-bold"><strong>Solution</strong></p>
<p>To find the \(x\)-intercept:<br>
  <strong>Step 1</strong> - Let \(y = 0\).<br>
\(2x + 0 = 8\)</p>
<p><strong>Step 2 </strong>- Solve for \(x\).<br>
\(x = 4\)</p>
<p><strong>Step 3</strong> - Write the intercept as a point.<br>
\((4,0)\)</p>
<br />
<p>To find the \(y\)-intercepts:<br>
  <strong>Step 1</strong> - Let \(x = 0\).<br>
\(2(0) + y = 8\)</p>
<p><strong>Step 2</strong> - Solve for \(y\).<br>
\(y=8\)</p>
<p><strong>Step 3 </strong>- Write the intercept as a point.<br>
\((0, 8)\)</p>
<br>

      
<h4>Try It: Finding Intercepts from Graphs and Equations</h4>
    <p>Find the \(x\)- and \(y\)-intercept of \(x+4y=8\).</p>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="eventShow1" data-schema-version="1.0">
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  <div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
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<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="eventShow1">
       <p>Compare your answer: (8, 0) (0, 2)</p>
  <p>Here is how to find the intercepts using a general strategy.</p>
<p>To find the \( x \)-intercept, <br>
  <strong>Step 1</strong> Let \( y=0 \).<br>
\( x+4(0)=8\)</p>
<p><strong>Step 2</strong> - Solve for \( x \).<br>
\(x = 8\)</p>
<p><strong>Step 3</strong> -  Write the intercept as a point.<br>
\((8, 0)\)</p>
<br>

<p>To find the \(y\)-intercept:<br>
  <strong>Step 1 </strong>- let \( x=0 \)<br>
\((0)+ 4y = 8\)</p>
<p><strong>Step 2</strong> - Solve for \( y \).<br>
\(y = 2\) </p>
<p><strong>Step 3</strong> - Write the intercept as a point.<br>
\((0, 2)\)</p>


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