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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<p>In questions 1-2, find the equation of a line with given slope and \( y \)-intercept. Write the equation in slope-intercept form.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="c3e16583-349e-4429-bc29-2d8c38bd2463" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--Enter Questions Below this line-->
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="8ef284c1-00ab-48a5-88e3-a507f9d890c1" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=3x+5\)" data-solution-options='["\\(y=5x+3\\)", "\\(y=3x+0\\)", "\\(y=3x+5\\)", "\\(y=0x+3\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>slope 3 and \( y \)-intercept \( ( 0,5) \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( y=3x+5 \) <br>
\(\begin{array}{rcl}y-y_1&=&m(x-x_1)\\y-(5)&=&3(x-(0))\\y-5&=&3(x)\\y-5&=&3x\\y&=&3x+5\\&&\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=3x+5\). </p>
<p>\(\begin{array}{rcl}y-y_1&=&m(x-x_1)\\y-(5)&=&3(x-(0))\\y-5&=&3(x)\\y-5&=&3x\\y&=&3x+5\\&&\end{array}\)</p>
</div>
</div>
<br>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="d44ab61a-84e5-4c4c-822b-3016c0730bf5" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-3x-1\)" data-solution-options='["\\(y=-x-3\\)", "\\(y=-3x-1\\)", "\\(y=-x+0\\)", "\\(y=0x-3\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>slope \(−3 \) and \( y \)-intercept \( (0,−1)\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( y=-3x-1 \)</p>
<p>\(\begin{array}{rcl}y-y_1&=&m(x-x_1)\\y-(-1)&=&-3(x-(0))\\y+1&=&-3(x)\\y+1&=&-3x\\y&=&-3x-1\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-3x-1\). </p>
<p>\(\begin{array}{rcl}y-y_1&=&m(x-x_1)\\y-(-1)&=&-3(x-(0))\\y+1&=&-3(x)\\y+1&=&-3x\\y&=&-3x-1\end{array}\)</p>
</div>
</div>
<br>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="22534ea5-e0df-44bb-82b5-d457a01de3a3" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=3x-5\)" data-solution-options='["\\(y=-3x+5\\)", "\\(y=5x-3\\)", "\\(y=-5x+3\\)", "\\(y=3x-5\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>In questions 3-4, Choose the slope-intercept form of the equation of the line, shown in each graph. </p>
<ol class="os-raise-noindent" start="3">
<li><br>
<img alt class="img-fluid atto_image_button_text-bottom" height="306" rule="presentation" src="https://k12.openstax.org/contents/raise/resources/09a02347b18374d51af8598355f5cf5524859116" width="300">
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( y=3x-5 \)</p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(1)-(-2)}{(2)-(1)}\\m&=&\frac{1+2}{2-1}\\m&=&\frac{3}{1}=3\end{array}\)</p>
<p>\(\begin{array}{rcl}y−y_1&=&m(x−x_1)\\y−(−2)&=&3(x−(1))\\y+2&=&3(x−1)\\y+2&=&3x−3\\y&=&3x−5\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=3x-5\). </p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(1)-(-2)}{(2)-(1)}\\m&=&\frac{1+2}{2-1}\\m&=&\frac{3}{1}=3\end{array}\)</p>
<p>\(\begin{array}{rcl}y−y_1&=&m(x−x_1)\\y−(−2)&=&3(x−(1))\\y+2&=&3(x−1)\\y+2&=&3x−3\\y&=&3x−5\end{array}\)</p>
</div>
</div>
<br>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="b4b0e8cb-bca8-4efe-860f-165f82fd0d0f" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-2x+4\)" data-solution-options='["\\(y=-2x+4\\)", "\\(y=2x+4\\)", "\\(y=\\frac12x -4\\)", "\\(y=\\frac12 x+2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li><br>
<img alt class="img-fluid atto_image_button_text-bottom" height="303" rule="presentation" src="https://k12.openstax.org/contents/raise/resources/eeae77b746d027b94298de1aaee697496e0d56a5" width="300">
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( y=-2x+4 \)</p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(4)-(0)}{(0)-(2)}\\m&=&\frac{4-0}{0-2}\\m&=&\frac{4}{-2}&=&-2\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (0) &=& −2(x − (2))\\y &=& −2(x − 2)\\y &=& −2x + 4\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-2x+4\). </p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(4)-(0)}{(0)-(2)}\\m&=&\frac{4-0}{0-2}\\m&=&\frac{4}{-2}&=&-2\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (0) &=& −2(x − (2))\\y &=& −2(x − 2)\\y &=& −2x + 4\end{array}\)</p>
</div>
</div>
<br>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="a0d8a289-e8c3-4a6f-b6aa-febc913fcfa0" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-7x-10\)" data-solution-options='["\\(y=-7x-1\\)", "\\(y=-7x-3\\)", "\\(y=-3x+10\\)", "\\(y=-7x-10\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Choose the equation of a line with the given
slope and containing the given point that best represents the line in
slope-intercept form. </li>
</ol>
<p> \(m=−7\), point \((−1,−3)\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( y=-7x-10 \)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (−3) &=& −7(x − (−1))\\y + 3 &=& −7(x + 1)\\y + 3 &=& −7x − 7\\y &=& −7x − 10\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-7x-10\). </p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (−3) &=& −7(x − (−1))\\y + 3 &=& −7(x + 1)\\y + 3 &=& −7x − 7\\y &=& −7x − 10\end{array}\)</p>
</div>
</div>
<br>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="988663d2-d0e1-4007-a583-801276ebffbe" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-\frac72x+4\)" data-solution-options='["\\(y=-\\frac72x-3\\)", "\\(y=\\frac72x+4\\)", "\\(y=-\\frac27x+4\\)", "\\(y=-\\frac72x+4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li>Choose the equation of a line containing the given points that best
represents the line in slope-intercept form. </li>
</ol>
<p> \((0,4)\) and \((2,−3)\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-\frac72x+4\)</p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(-3)-(4)}{(2)-(0)}\\m&=&\frac{-3-4}{2-0}\\m&=&\frac{-7}{2}\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (4) &=& -\frac{7}{2}(x − (0))\\y − 4 &=& -\frac{7}{2}(x)\\y &=& -\frac{7}{2}x + 4\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-\frac72x+4\). </p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(-3)-(4)}{(2)-(0)}\\m&=&\frac{-3-4}{2-0}\\m&=&\frac{-7}{2}\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (4) &=& -\frac{7}{2}(x − (0))\\y − 4 &=& -\frac{7}{2}(x)\\y &=& -\frac{7}{2}x + 4\end{array}\)</p>
</div>
</div>
<br>
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="1ddea227-6cfa-401e-9c34-d66382305700" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-4\)" data-solution-options='["\\(y=-4\\)", "\\(y=0\\)", "\\(x=2\\)", "\\(x=-2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>Choose the equation of a line containing the given points
that best represents the line in slope-intercept form.</li>
</ol>
<p>\((3,−4)\) and \((5,−4)\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-4\)</p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(-4)-(-4)}{(5)-(3)}\\m&=&\frac{-4+4}{5-3}\\m&=&\frac{0}{2}=0\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (−4) &=& 0(x − (3))\\y + 4 &=& 0(x − 3)\\y &=& −4\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-4\). </p>
<p>\(\begin{array}{rcl}m&=&\frac{y_2-y_1}{x_2-x_1}\\m&=&\frac{(-4)-(-4)}{(5)-(3)}\\m&=&\frac{-4+4}{5-3}\\m&=&\frac{0}{2}=0\end{array}\)</p>
<p>\(\begin{array}{rcl}y − y_1 &=& m(x − x_1)\\y − (−4) &=& 0(x − (3))\\y + 4 &=& 0(x − 3)\\y &=& −4\end{array}\)</p>
</div>
</div>
<br>
<!--Q#-->
<div class="os-raise-ib-pset-problem" data-content-id="0d4df168-9815-422a-b8fe-790cdafe44fc" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(3x - y =1\)" data-solution-options='["\\(y=3x-1\\)", "\\(-3x+y = -1 \\)", "\\(3x - y =1\\)", "\\(y=3x -11\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>Which of the following equations is
\(y-5=3(x-2)\) written in standard form? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p>\(\begin{array}{rcl}y-5&=&3(x-2)\\y-5&=&3x-6\\y-5+5&=&3x-6+5\\y&=&3x-1\\y-3x&=&3x-3x-1\\-3x +y&=&-1\\\frac{-3x}{ -1}+\frac{y}{-1}&=&{-1}{-1}\\3x - y &=&1\end{array}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.12.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(3x - y =1\). </p>
</div>
</div>
<!--Q#9-->
<div class="os-raise-ib-pset-problem" data-content-id="c345c099-f334-4829-a6f2-07a7c7ebcf82" data-problem-type="multiplechoice" data-solution="\(y-2=3(x-4)\)" data-solution-options='["\\(y-2=3(x-4)\\)", "\\(y-4=-3(x+2)\\)", "\\(y+2=\\frac13(x-4)\\)", "\\(y-4=3(x-2)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>Write the equation of a line that contains the points \((–3,–1)\) and \((2,–2)\). Write the equation in point-slope form.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y-2=3(x-4)\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#10-->
<div class="os-raise-ib-pset-problem" data-content-id="1793fb44-9898-4e66-9783-3eb4a0f4b282" data-problem-type="multiplechoice" data-solution="\(8x-y=19\)" data-solution-options='["\\(8x - y = -19 \\)", "\\(8x + y = 19\\)", "\\(8x-y=19\\)", "\\( 19x + y = 8\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<li>Write the equation of a line that contains the point (2, -3) with a slope of 8. Write the equation in standard form.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(8x-y=19\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#11-->
<div class="os-raise-ib-pset-problem" data-content-id="545e7634-a60f-48dc-aa3e-fc69ccc363d6" data-problem-type="multiplechoice" data-solution="\(x+y=4\)" data-solution-options='["\\(x - y = 4 \\)", "\\(x+y=4\\)", "\\(-x+y = 4\\)", "\\(x + y = -4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11">
<li>Write the equation of a line that contains the points (3, 1) and (-1, 5). Write the equation in standard form. </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(x+y=4\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>