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<h3>Modeling Linear Equations</h3>
<p>Given a real-world problem, model a linear equation to fit it using these steps:</p>
<p><strong>Step 1</strong> - Read the problem.</p>
<p><strong>Step 2</strong> - Identify the variables and known values. If needed, sketch a picture of the scenario. </p>
<p><strong>Step 3</strong> - Write a sentence or create a table using the relationship among the values. </p>
<p><strong>Step 4</strong> - Translate the sentence or table into an equation</p>
<br><p>Let’s look at an example. Using the steps above, we can model a linear equation to solve a real-world application.</p>
<strong>Example
</strong>
<p>Cell phone Company A charges a monthly service fee of $34 plus $0.05/minute talk time.</p>
<p><strong>Step 1</strong> - Read the problem.</p>
<p>Cell phone Company A charges a monthly service fee of $34 plus $0.05/minute talk time.</p>
<p><strong>Step 2</strong> - Identify the variables and known values. If needed, sketch a picture of the scenario.</p>
<p>\(t\): total cost (in dollars)<br>
\(m\): number of minutes
</p>
<p><strong>Step 3</strong> - Write a sentence or create a table using the relationship among the values.</p>
<table class="os-raise-horizontaltable">
<caption>Company A:</caption>
<thead></thead>
<tbody>
<tr>
<th scope="row">
Minutes Talked in One Month
</th>
<td>
0
</td>
<td>
1
</td>
<td>
2
</td>
<td>
3
</td>
<td>
100
</td>
</tr>
<tr>
<th scope="row">
Total for One Month (Dollars)
</th>
<td>
34
</td>
<td>
34.05
</td>
<td>
34.10
</td>
<td>
34.15
</td>
<td>
39
</td>
</tr>
</tbody>
</table><br>
<p>Company A: The total cost, \(t\), equals the fee, 34, plus 0.05 per minute, \( 0.05m \).</p>
<p><strong>Step 4</strong> - Translate the sentence or table into an equation.<br>
\(t = 34 + 0.05m\)</p>
<h4>Try It: Modeling Linear Equations</h4>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="83dea92d-4a16-4ee9-bb6f-243e40c29626" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Cell phone Company B charges a monthly service fee of $40 plus $0.04/min talk-time. Write an equation to describe
the relationship between the number of minutes and the total cost.</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><strong>Step 1</strong> - Read the problem.</p>
<p>Cell phone Company B charges a monthly service fee of $40 plus $0.04/minute talk time. Write an equation to describe the relationship between the number of minutes and the total cost.
</p>
<p><strong>Step 2</strong> - Identify the variables and known values. If needed, sketch a picture of the scenario.
</p>
<p>Monthly Fee: $40, Cost per Minute: $0.04</p>
<p>\(t\): total cost (in dollars)<br>
\(m\): number of minutes</p>
<p><strong>Step 3</strong> - Write a sentence or create a table using the relationship among the values.</p>
<p>Company B:</p>
<table class="os-raise-horizontaltable">
<thead></thead>
<tbody>
<tr>
<th scope="row">
Minutes Talked in One Month
</th>
<td>
0
</td>
<td>
1
</td>
<td>
2
</td>
<td>
3
</td>
<td>
100
</td>
</tr>
<tr>
<th scope="row">
Total for One Month (Dollars)
</th>
<td>
40
</td>
<td>
40.04
</td>
<td>
40.08
</td>
<td>
40.12
</td>
<td>
44
</td>
</tr>
</tbody>
</table>
<br>
<p>The total cost, \(t\), equals the fee, 40, plus 0.04 per minute.</p>
<p>Step 4 - Translate the sentence or table into an equation.<br>
\(t = 40 + 0.04m\)
</p>
</div>
</div>
<!--Interaction End -->