f5e4ef9f-16c2-4db9-bd5a-c57c0f4cfa05.html

<h3>Cool Down (10 minutes)</h3>
<h4>Activity</h4>
<p>With a partner, use what you have learned to write an equation in each form from two points.</p>
<ol class="os-raise-noindent">
  <li> Find the slope of the line that goes through \((2,3)\) and \((6,-4)\). </li>
</ol>
<p><strong>Answer:</strong> \(-\frac74\)</p>
<p>\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-3}{6-2}=-\frac74\)</p>
<ol  class="os-raise-noindent" start="2">
  <li> Write the equation of the line in point-slope form that goes through \((2,3) \)and \((6,-4)\). </li>
</ol>
<p><strong>Answer:</strong> \(y-3=-\frac{7}{4}(x-2)\) or \(y+4=-\frac{7}{4}(x-6)\)</p>
<p>Using the point \((2,3)\):</p>
<p>\(y-y_1=m(x-x_1)\)</p>
<p>\(y-3=-\frac{7}{4}(x-2)\)</p>
<p>Using the point \((6, -4)\):</p>
<p>\(y-y_1=m(x-x_1)\)</p>
<p>\(y-(-4)=-\frac{7}{4}(x-6)\)</p>
<p>\(y+4=-\frac{7}{4}(x-6)\)</p>
<ol  class="os-raise-noindent" start="3">
  <li> Write the equation of the line in slope-intercept form that goes through \((2,3)\) and \((6,-4)\). (Hint: use the equation from number 2) </li>
</ol>
<p><strong>Answer:</strong> \(y=-\frac{7}{4}x+\frac{13}{2}\)</p>
<p>\(y-3=-\frac{7}{4}(x-2)\)</p>
<p>\(y-3=-\frac{7}{4}x+\frac{14}{4}\)</p>
<p>\(y-3=-\frac{7}{4}x+\frac72\)</p>
<p>\(y-3+3=-\frac{7}{4}x+\frac{7}{2}+3\)</p>
<p>\(y=-\frac{7}{4}x+\frac{7}{2}+\frac{6}{2}\)</p>
<p>\(y=-\frac{7}{4}x+\frac{13}{2}\)</p>
<ol start="4">
  <li> Write the equation of the line in standard form that goes through \((2,3)\) and \((6,-4)\). </li>
</ol>
<p>(Hint: use the equation from number 3.)</p>
<p><strong>Answer:</strong> \(7x+4y=26\)</p>
<p>\(4(y=-\frac{7}{4}x+\frac{13}{2})\)</p>
<p>\(4y=-7x+26\)</p>
<p>\(4y+7x=-7x+7x+26\)</p>
<p>\(7x+4y=26\)</p>
<h4>Response to Student Thinking</h4>
<h5>More Chances</h5>
<p>If students are struggling with the concepts, pay close attention during the cool down and provide assistance where needed. Students will have more time in 4.8 to explore finding slope using the slope formula as a way to find the rate of change.</p>