14aad2e5-518c-4921-8a63-627dbbf82733.html

<h4>Warm Up (5 minutes)</h4>
<p>The purpose of this warm up is to help students recall finding the equation of a line given the slope and a point on the line. The lines are designed to facilitate discussions about lines with the same slope and different \(y\)-intercepts to prepare for work with parallel lines.</p>
<h4>Launch</h4>
<p>Have students work in pairs. Assign the information for Line A to one of the partners and the information for Line B to the other partner. Give students a couple of minutes to find the slope and equation of the line.</p>
<h4>Student Activity</h4>
<p>Your teacher will assign you one pair of the points shown.</p>
<p>Points for Line A: \( (-1, 5) \) and \( (1, 1) \)<br>
  Points for Line B: \( (-1, -1) \) and \( (1, -5) \)</p>
<p>Use your assigned points to find the following:</p>
<ol class="os-raise-noindent">
  <li>Find the slope of the line.</li>
</ol>
<p><strong>Answer:</strong> </p>
<p>Line A: slope: \( m= \frac{1-5}{1-(-1)}=-2 \)<br>
  Line B: slope: \( m= \frac{-5-(-1)}{1-(-1)}=-2 \)</p>
<ol class="os-raise-noindent" start="2">
  <li> Write the equation of the line in slope-intercept form.</li>
</ol>
<p><strong>Answer:</strong> </p>
<p>Line A: equation \( y = -2x + 3 \)<br>
  Line B: equation \( y = -2x - 3 \)</p>
<p>Remember to use the point-slope form for the equation of the line to write the equation: \( y - y_1 = m_1(x - x_1) \). Write the equation in slope-intercept form \( y = mx + b \), where the slope is \( m \) and the \( y \)-intercept is \( b \).</p>
<p>Remember to use the slope formula to find the slope: \( m=\frac{y_2-y_1}{x_2-x_1} \).</p>
<ol class="os-raise-noindent" start="3">
  <li>Compare your equation to your partner’s equation. What were some things that were the same? What were some things that were different?</li>
</ol>
<p><strong>Answer:</strong> Your answer may vary, but here are some samples. </p>
<ul>
  <li>Both lines have a negative slope.</li>
  <li>Both lines have the same slope.</li>
  <li>The \( y \)-intercepts are different. </li>
  <li>The \( y \)-intercepts have opposite signs.</li>
</ul>
<br>
<h4>Anticipated Misconceptions</h4>
<p>Students may mistakenly find the change in \( x \) over the change in \(y\) when finding the slope. There is a lot of room for error using the point-slope form of the equation of the line. Students may mistakenly substitute the given \( x \)-value for \( y_1 \) and the given \( y \)-value for \( x_1 \). Students may also make errors using the distributive property or may make sign errors when simplifying. Students may think the \( y \)-intercepts are the same because they see the &ldquo;3&rdquo; and do not realize in Line B, the 3 is negative.</p>
<h4>Activity Synthesis</h4>
<p>Ask a few students from each group for their results. Have students share the method they used to write the equation of the line. Then, ask students what they wonder about the results. Students may notice the slopes are the same and the \( y \)-intercepts are different. </p>
<p>Ask students: </p>
<ul>
  <li>What does the graph of a line with a negative slope look like?</li>
  <li>What does the graph of a line with a positive slope look like?</li>
  <li>What does the slope of the line mean on the graph?</li>
  <li>What do you think two lines with the same slope will look like on the graph?</li>
  <li>If time allows, have the students graph the lines to see how they compare. This will help introduce the next topic of parallel lines. </li>
</ul>