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<h4>Writing Linear Equations in Different Forms</h4>
<p class="os-raise-text-bold">Example 1</p>
<p>When you look at equations in these forms, it's easy to identify the slope of \(m\).</p>
<table class="os-raise-wideequaltable">
  <thead>
    <tr>
      <th scope="col">Equation</th>
      <th scope="col">Equation Formula</th>
      <th scope="col">Slope Formula</th>
      <th scope="col">Slope Value</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>\(y=5x-15\)</td>
      <td>\(y=mx+b\)</td>
      <td>\(m\)</td>
      <td>5</td>
    </tr>
    <tr>
      <td>\(y=6x+8\)</td>
      <td>\(y=mx+b\)</td>
      <td>\(m\)</td>
      <td>6</td>
    </tr>
    <tr>
      <td>\(y−7=9(x+1)\)</td>
      <td>\(y−y_1=m(x−x_1)\)</td>
      <td>\(m\)</td>
      <td>9</td>
    </tr>
    <tr>
      <td>\(y-20=3(x+16)\)</td>
      <td>\(y-y_1=m(x-x_1)\)</td>
      <td>\(m\)</td>
      <td>3</td>
    </tr>
    <tr>
      <td>\(18x - 6y = 24\)</td>
      <td>\(Ax + By = C\)</td>
      <td>\(m = -\frac AB\)</td>
      <td> \(-(\frac {18}{-6})= 3\)</td>
    </tr>
    <tr>
      <td>\(30x + 15y = 24\)</td>
      <td>\(Ax + By = C\)</td>
      <td>\(m = -\frac AB\)</td>
      <td>\(-\frac{30}{15}= -2\)</td>
    </tr>
  </tbody>
</table>
<br>
<p class="os-raise-text-bold">Example 2</p>
<p>Find the equation of a line with slope &minus;9 and \(y\)-intercept \((0,&minus;4)\) in slope-intercept form.</p>
<p><strong>Step 1 </strong>- Identify the \(m\) and \(b\).<br>
  \(m = -9\), \(b = -4\)</p>
<p><strong>Step 2</strong> - Substitute into the formula.<br>
  \(y = -9x - 4\)</p>
<br>
<p class="os-raise-text-bold">Example 3</p>
<p>Find the equation of a line in point-slope form given a slope of \(-\frac13\) and the point \((6,-4)\)</p>
<p><strong>Step 1</strong> - Identify the \(m\) and \((x_1,y_1)\).<br>
  \(m = -\frac{1}{3} x_1=6 y_1= -4\)</p>
<p><strong>Step 2</strong> - Substitute into the formula.<br>
  \(y-(-4)=-\frac{1}{3}(x-6)\)</p>
<p><strong>Step 3</strong> - Simplify<br>
  \(y+4=-\frac{1}{3}(x-6)\)</p>
<br>
<p class="os-raise-text-bold">Example 4</p>
<p>Write the equation \(y+4=-\frac{1}{3}(x-6)\) in standard form.</p>
<p><strong>Step 1</strong> - Multiply to get rid of the fraction.<br>
  Remember, standard form cannot have decimals or fractions.<br>
  Multiply every term by 3.<br>
  \(3(y+4)=3(-\frac{1}{3}(x-6))\)<br>
  \(3y+12=-(x-6)\)</p>
<p><strong>Step 2</strong> - Distribute.<br>
  \(3y+12=-x+6\)</p>
<p><strong>Step 3</strong> - Rearrange terms so the \(x\) term and the \(y\) term are both on the left side of the equation.<br>
  Add \(x\) to both sides.<br>
  \(3y+12+x=-x+x+6\)</p>
<p><strong>Step 4</strong> - Simplify.<br>
  \(3y+12+x=6\)</p>
<p><strong>Step 5</strong> - Bring the constants to the right side.<br>
  Subtract 12 from both sides.<br>
  \(3y+12+x-12=6-12\)</p>
<p><strong>Step 6 </strong>- Simplify.<br>
  \(3y+x=-6\)</p>
<p><strong>Step 7</strong> - Write the \(x\) term before the \(y\) term.<br>
  \(3x+y=-6\)</p>
<br>
<br>
<h4>Try It: Writing Linear Equations in Different Forms</h4>
<br>
<!--Q#-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="84402d7d-cb85-4070-8f50-4227e8cccaf2" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <p>Write the equation \(y-3=2(x+5)\) in standard form.</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: \(2x-y=-13\)</p>
    <br>
    <p><strong>Step 1</strong> - Distribute.<br>
      \(y-3=2x+10\)</p>
    <p><strong>Step 2</strong> - Rearrange terms so the \(x\) term and the \(y\) term are both on the left side of the equation.<br>
      Subtract \(2x\) from both sides.<br>
      \(y-3-2x=2x-2x+10\)</p>
    <p><strong>Step 3</strong> - Simplify.<br>
      \(y-3-2x=10\)</p>
    <p><strong>Step 4</strong> - Bring the constants to the right side.<br>
      Add 3 to both sides.<br>
      \(y-3-2x+3=10+3\)</p>
    <p><strong>Step 5</strong> - Simplify.<br>
      \(y-2x=13\)</p>
    <p><strong>Step 6</strong> - Write the \(x\) term before the \(y\) term.<br>
      \(-2x+y=13\)</p>
    <p><strong>Step 7</strong> - Multiply each term by -1.<br>
      Standard form cannot lead with a negative.<br>
      \(-1(-2x+y=13)\)</p>
    <p><strong>Step 8</strong> - Simplify.<br>
      \(2x-y=-13\)</p>
  </div>
</div>
<!--Interaction End -->