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<h4>Find an Equation of the Line Given Two Points</h4>
<p>So far, you have two options for finding an equation of a line: slope-intercept or point-slope. When you start with two points, it makes more sense to use the point-slope form.</p>
<p>But then you need the slope. You can find the slope with just two points and then use it and one of the given points to find the equation.</p>
<p><strong>Example</strong></p>
<p>Write the equation of a line that contains the points \( (&ndash;3, &ndash;1) \) and \( (2, &ndash;2) \). Write the equation in slope-intercept form and standard form.</p>
<p><strong>Step 1 -</strong> Find the slope using the given points.<br>
Find the slope of the line through \( (&ndash;3, &ndash;1) \) and \( (2, &ndash;2) \). <br>
\( m = \frac{y_2 - y_1}{x_2 -x_1} \) <br>
\( m = \frac{-2 - (-1)}{2-(-3)} \) <br>
\( m = \frac{-1}{5} \)<br>
\( m = - \frac{1}{5} \)</p>
<p><strong>Step 2 -</strong> Choose one point. <br>
Choose either point.<br>
\( (x_1, y_1) \)<br>
\( (2, &ndash;2) \) </p>
<p><strong>Step 3 - </strong>Substitute the values into the point-slope form, \( y - y_1 = m(x - x_1) \). <br>
Simplify<br>
\( \begin{array}{rcl}y-y_1&amp;=&amp;m(x-x_1)\\y-(-2)&amp;=&amp;-\frac15(x-2)\\y+2&amp;=&amp;-\frac15x+\frac25\end{array} \) </p>
<p><strong>Step 4 -</strong> Write the equation in slope-intercept form. <br>
\( y = -\frac{1}{5}x - \frac{8}{5} \)</p>
<p><strong>Step 5 -</strong> Convert slope-intercept form to standard form. <br>
\(y=−\frac15x−\frac85\)<br>
\(\frac15x+ y= −\frac85\)<br>
\(5(\frac15x+ y)=5(−\frac85)\)<br>
\((1x+ 5y)= −8\)</p>
<p><br>Use this table for easy reference to find an equation of a line given two points.</p>
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<p><strong>Step 1</strong> - Find the slope using the given points. <br>
\( m = \frac{y_2 - y_1}{x_2 -x_1} \) </p>
<p><strong>Step 2</strong> - Choose one point.</p>
<p><strong>Step 3</strong> - Substitute the values into the point-slope form: \( y - y_1 = m(x - x_1) \).</p>
<p><strong>Step 4</strong> - Write the equation in slope-intercept form. </p>
    <p><strong>Step 5 -</strong> Convert slope-intercept form to standard form.</p>
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<p><br>To find an equation of a line given the slope and a point, follow these steps:</p>
<p><strong>Step 1</strong> - Identify the slope.</p>
<p><strong>Step 2</strong> - Identify the point.</p>
<p><strong>Step 3</strong> - Substitute the values into the point-slope form, \( y - y_1 = m(x - x_1) \).</p>
<p><strong>Step 4</strong> - Write the equation in slope-intercept form.</p>
<p><strong>Step 5 -</strong> Convert slope-intercept form to standard form.</p></div>
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<h4>Try It: Writing the Equation of a Line Given Two Points</h4>


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<p>Write the equation of a line that contains the points&nbsp;\( (-3, 5) \) and \( (-3, 4) \).</p>
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<p>Write down your answer, and then select the <strong>solution</strong> button to compare your work.</p>
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 <p>Here is how to find an equation of a line that contains the points \( (&ndash;3, 5) \) and \( (&ndash;3, 4) \).</p>
<p>Again, the first step will be to find the slope.</p>
<p><strong>Step 1</strong> - Find the slope of the line through \( (&ndash;3, 5) \) and \( (&ndash;3, 4) \).</p>
<p><strong>Step 2</strong> - \( m = \frac{y_2 - y_1}{x_2 -x_1} \) </p>
<p><strong>Step 3</strong> - \( m = \frac{4-5}{-3-(-3)} \) </p>
<p><strong>Step 4</strong> - \( m = \frac{-1}{0} \)</p>
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<p>A line with undefined slope is a vertical line. Both given points have an \( x \)-coordinate of \( &ndash;3 \). So, the equation of the line is \( x = -3 \). There is no \( y \), so the equation cannot be written in slope-intercept form.<br></p>
  
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