5242716e-f450-49ba-b9c9-b6a6d8f6351d.html

<h4>Writing Linear Equations from Tables</h4>
<p>When writing linear equations from tables, it is important to identify the slope and the \(y\)-intercepts from the table.</p>
<p><strong>Example</strong></p>
<p>Given the table, write an equation in slope-intercept form.</p>
<table class="os-raise-horizontaltable">
  <thead>
  </thead>
  <tbody>
    <tr>
      <th scope="row">\(x\)</th>
      <td>0</td>
      <td>1</td>
      <td>2</td>
      <td>3</td>
      <td>4</td>
    </tr>
    <tr>
      <th scope="row">\(y\)</th>
      <td>12</td>
      <td>16</td>
      <td>20</td>
      <td>24</td>
      <td>28</td>
    </tr>
  </tbody>
</table>
<br>
<p><strong>Step 1</strong> - Identify the \(y\)-intercept.</p>
<p>The \(y\)-intercept is the starting value, when \(x=0\).<br>
  Looking at the table, when \(x = 0\), the \(y\)-value is 12, so this is the \(y\)-intercept.</p>
<p><strong>Step 2</strong> - Identify the slope.</p>
<p>Slope is the change in \(y\) over the change in \(x\).<br>
  The \(y\)-values change by 4 each time. The \(x\)-values change by 1 each time.</p>
<p>The slope is \(\frac41\) or 4.</p>
<p><strong>Step 3</strong> - Write the equation in slope-intercept form.</p>
<p>Slope intercept form is \(y = mx +b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.<br>
  Substitute the values, \(y = 4x +12\).</p>
<br>
<h4>Try It: Writing Linear Equations from Tables</h4>
<br>
<!--Q#-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="108dcee2-9ccb-4333-94d7-a2282a04cf84" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <p>Given the table, write an equation in slope-intercept form.</p>
    <table class="os-raise-horizontaltable">
      <thead>
      </thead>
      <tbody>
        <tr>
          <th scope="row">\(x\)</th>
          <td>0</td>
          <td>1</td>
          <td>2</td>
          <td>3</td>
        </tr>
        <tr>
          <th scope="row">\(y\)</th>
          <td>6</td>
          <td>11</td>
          <td>16</td>
          <td>21</td>
        </tr>
      </tbody>
    </table>
    <br>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter your answer here:</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>Here is how to write the equation in slope-intercept form:</p>
    <p><strong>Step 1</strong> - Identify the \(y\)-intercept.</p>
    <p>The \(y\)-intercept is the starting value, when \(x=0\).<br>
      Looking at the table, when \(x = 0\), the \(y\)-value is 6, so this is the \(y\)-intercept.</p>
    <p><strong>Step 2</strong> - Identify the slope.</p>
    <p>Slope is the change in \(y\) over the change in \(x\).<br>
      The \(y\)-values change by 5 each time. The \(x\)-values change by 1 each time.<br>
      The slope is \(\frac51\) or 5.</p>
    <p><strong>Step 3</strong> - Write the equation in slope-intercept form.</p>
    <p>Slope intercept form is \(y = mx +b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.<br>
      Substitute the values, \(y = 5x +6\).</p>
  </div>
</div>
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