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<h4>Writing Linear Equations From Tables and Graphs</h4>
<p>Linear Equations from Tables</p>
<p>The number of texts a teen sends, \(T\), in days, \(d\), is shown in the table below.</p>
<table class="os-raise-horizontaltable">
  <thead>
  </thead>
  <tbody>
    <tr>
      <th scope="row">Days, \(d\)</th>
      <td>1</td>
      <td>2</td>
      <td>3</td>
      <td>4</td>
    </tr>
    <tr>
      <th scope="row">Number of texts, \(T|)</th>
      <td>65</td>
      <td>130</td>
      <td>195</td>
      <td>260</td>
    </tr>
  </tbody>
</table>
<br>
<p>Write an equation in slope-intercept form to represent the situation then predict the number of texts sent in 8 days.</p>
<p><strong>Step 1</strong> - Find the \(y\)-intercept.<br>
  Since the value when \(d=0\) is not present, work backwards to \(d=0\).&nbsp;<br>
  If \(d=0\) was present, then \(T=0\) since as each x-value increases by 1, the \(y\)-values increase by 65.</p>
<p><strong>Step 2</strong> - Find the slope of the situation.<br>
  Find the rate of change. The change in y is 65 and the change in \(x\) is 1, so the slope is 65</p>
<p><strong>Step 3</strong> -Write the equation in slope-intercept form.<br>
  \(y=mx+b\)<br>
  \(T=65d +0\)<br>
  \(T=65d\)</p>
<p><strong>Step 4 </strong>-Make a prediction.<br>
  Substitute \(d=8\) into the equation.<br>
  \(T=65(8)=520\)</p>
<p>After 8 days, the teen would have sent 520 texts.</p>
<br>
<p><strong>Linear Equations from Graphs</strong></p>
<p>The cost, C, for the number of days, \(d\), a dog spends at doggie daycare is shown in the graph below.<br>
  <img src="https://k12.openstax.org/contents/raise/resources/3f66172ff755fe8a3f00243f3a79bb981754dab1" width="300">
</p>
<p>Write an equation in slope-intercept form to represent the situation then predict the cost of a dog staying at doggie daycare after 7 days.</p>
<p><strong>Step 1 </strong>- Find the \(y\)-intercept.<br>
  Since the value when \(d=0\) is not present, work backwards to \(d=0\).&nbsp;<br>
  If \(d=0\) was present, then \(C=0\) since as each \(x\)-value increases by 1, the \(y\)-values increase by 35.</p>
<p><strong>Step 2 </strong>- Find the slope of the situation.<br>
  Find the rate of change. The change in \(y\) is 35 and the change in \(x\) is 1, so the slope is 35</p>
<p><strong>Step 3</strong> -Write the equation in slope-intercept form.<br>
  \(y=mx+b\)<br>
  \(C=35d +0\)<br>
  \(C=35d\)</p>
<p><strong>Step 4</strong> -Make a prediction.<br>
  Substitute \(d=7\) into the equation.<br>
  \(C=35(7)=245\)</p>
<br>
<p>After 7 days, the cost of doggie daycare would be $245.</p>
<br>
<h4>Try It-Writing Linear Equations From Tables and Graphs</h4>
<p>Naomi is a professional painter. The table below shows how many square feet, \(F\), she can paint in \(h\) hours.</p>
<table class="os-raise-horizontaltable">
  <thead>
  </thead>
  <tbody>
    <tr>
      <th scope="row">Time in hours, \(h\)</th>
      <td>1</td>
      <td>2</td>
      <td>3</td>
      <td>4</td>
    </tr>
    <tr>
      <th scope="row">Number of square feet, \(F\)</th>
      <td>120</td>
      <td>240</td>
      <td>360</td>
      <td>480</td>
    </tr>
  </tbody>
</table>
<br>
<br>
<!--Q#-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2cafe294-0a9e-4289-b5a6-10b5213f483f" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <p>How many square feet can Naomi paint in 8 hours?</p>
  </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>960</p>
    <p><strong>Step 1</strong> - Find the \(y\)-intercept.<br>
      Since the value when \(h=0\) is not present, work backwards to \(h=0\).&nbsp;<br>
      If \(h=0\) was present, then \(F=0\) since as each \(x\)-value increases by 1, the \(y\)-values increase by 120.</p>
    <p><strong>Step 2</strong> - Find the slope of the situation.<br>
      Find the rate of change. The change in \(y\) is 120 and the change in \(x\) is 1, so the slope is 120</p>
    <p><strong>Step 3</strong> -Write the equation in slope-intercept form.<br>
      \(y=mx+b\)<br>
      \(F=120h+0\)<br>
      \(F=120h\)</p>
    <p><strong>Step 4</strong> -Make a prediction.<br>
      Substitute \(h=8\) into the equation.<br>
      \(F=120(8)=960\)</p>
    <p>Naomi can paint 960 square feet in 8 hours.</p>
  </div>
</div>
<!--Interaction End -->
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