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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<blockquote>
<p>In questions 1 - 5, choose an equation of a line parallel to the given line and contains the given point. The choices are in slope-intercept form.</p>
</blockquote>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="16edde3f-4bd7-4329-a8de-43c9e2bd357c" 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="909f5114-1beb-4172-83b5-3cfc322d081c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=4x-2\)" data-solution-options='["\\(y=4x+2\\)", "\\(y=4x-2\\)", "\\(y=-\\frac14x-2\\)", "\\(y=-\\frac14x+2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>Line \(y = 4x + 2\)<br>
Point
\((1, 2)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=4x-2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y = 4 x -2\). </p>
<p>The slope of a line parallel to \(y = 4x + 2\) is 4. The line contains the point (1,2).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (2) &= 4(x − (1))\\
y − 2 &= 4(x − 1)\\
y − 2 &= 4x − 4\\
y &= 4x − 2
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="61d898ac-c69c-4b32-8003-4768a55fa342" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-3x +3\)" data-solution-options='["\\(y=-3x +3\\)", "\\(y=-3x-3\\)", "\\(y=\\frac13x+3\\)", "\\(y=\\frac13x-3\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>Line \(y = -3x -1\)<br>
Point \((2, -3)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-3x +3\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y = -3x +3\). </p>
<p>The slope of a line parallel to \(y = −3x − 1\) is \(−3\). The line contains the point (2,−3).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (-3) &= −3(x − (2))\\
y + 3 &= −3(x − 2)\\
y +3 &= −3x + 6\\
y &= −3x +3
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="39322255-26c6-4b83-98b0-7e16753f6a4c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=2x-6\)" data-solution-options='["\\(y=2x\\)", "\\(y=-2x+6\\)", "\\(y=-2x\\)", "\\(y=2x-6\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Line \(2x - y = 6\)<br>
Point \((3, 0)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=2x-6\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=2x-6\). </p>
<p>The slope of a line parallel to \(2x −y = 6\) is 2. The line contains the point (3,0).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (0) &= 2(x − (3))\\
y &= 2(x − 3)\\
y &= 2x − 6\\
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="72376f8b-6771-4aa4-8484-40c9d04b1f19" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(x=-3\)" data-solution-options='["\\(x=-3\\)", "\\(y=-5\\)", "\\(x=-5\\)", "\\(y=-4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>Line \(x = -4\)<br>
Point \((-3, -5)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=-3\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(x=-3\). </p>
<p> The slope of a line parallel to \(x = −4\) is undefined. The line contains the point (−3,−5).<br>
The only equation with an undefined slope passing through (−3,−5) is \(x = −3\).</p>
<br>
</div>
</div>
<br>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="e11b16ef-f53c-40c9-bf63-f5f54930aa72" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-2\)" data-solution-options='["\\(x=2\\)", "\\(x=5\\)", "\\(y=-2\\)", "\\(y=2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Line \(y = 5\)<br>
Point \((2, -2)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-2\). </p>
<p>The slope of a line parallel to \(y = 5\) is 0. The line contains the point (2,−2).<br>
The only equation with a slope of 0 passing through (2, −2) is \(y = −2\).</p>
</div>
</div>
<br>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="5980b1f7-cf0a-4fbc-94a4-7a42d531e127" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=\frac12x+1\)" data-solution-options='["\\(y=-2x+6\\)", "\\(y=-\\frac12x+3\\)", "\\(y=\\frac12x+3\\)", "\\(y=\\frac12x+1\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<blockquote>
<p>In questions 6–10, find an equation of a line that is perpendicular to the given line and contains the given point. The choices are in slope-intercept form.</p>
</blockquote>
<ol class="os-raise-noindent" start="6">
<li>Line \(y = -2x +3\)<br>
Point \((2, 2)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=\frac12x+1\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=\frac12x+1\). </p>
<p>TThe slope of a line perpendicular to \(y = −2x + 3\) is \(\frac12\). The line contains the point (2,2).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (2) &= \frac12(x − (2))\\
y −2 &= \frac12(x − 2)\\
y −2 &= \frac12x − 1\\
y &= \frac12x + 1
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="34f5f688-d8a6-44c9-ad20-c0035d7de4f2" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=x\)" data-solution-options='["\\(y=-x+6\\)", "\\(y=x\\)", "\\(y=x+5\\)", "\\(y=-x+3\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>Line \(y = -x +5\)<br>
Point \((3, 3)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=x\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=x\). </p>
<p>The slope of a line perpendicular to \(y = −x + 5\) is 1. The line contains the point (3,3).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (3) &= 1(x − (3))\\
y − 3 &= 1(x − 3)\\
y − 3 &= x − 3\\
y &= x \\
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q8-->
<div class="os-raise-ib-pset-problem" data-content-id="3854c9ff-58ec-4025-9fbb-4ee11fad4cae" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-\frac43x\)" data-solution-options='["\\(y=-\\frac43x\\)", "\\(y=-\\frac43x+4\\)", "\\(y=\\frac34x+4\\)", "\\(y=\\frac34x+\\frac{17}4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>Line \(y = \frac{3}{4}x - 2\)<br>
Point \((-3, 4)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-\frac43x\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-\frac43x\). </p>
<p> The slope of a line perpendicular to \(y = \frac34x − 2\) is \(−\frac43.\) The line contains the point (−3,4).</p>
<!--BEGIN ALIGN TO EQUALS-->
<p>\(\begin{aligned}y − y_1 &= m(x − x_1)\\
y − (4) &= −\frac43(x − (−3))\\
y −4 &= −\frac43(x + 3)\\
y −4 &= −\frac43x − 4\\
y &= −\frac43x
\end{aligned}\)</p>
<!--END ALIGN TO EQUALS -->
</div>
</div>
<br>
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="69dbb715-5c57-4a0a-b43b-7937bcb9423c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(y=-2\)" data-solution-options='["\\(y=-5\\)", "\\(x=1\\)", "\\(y=-2\\)", "\\(x=-2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>Line \(x = -5\)<br>
Point \((1, -2)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(y=-2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(y=-2\). </p>
<p>The slope of a line perpendicular to \(x = −5\) is 0. The line contains the point (1,−2).<br>
The only equation with a slope of 0 passing through (1,−2) is y \(= −2\).</p>
</div>
</div>
<br>
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="61146fd3-06de-4520-a2b4-fc2d65f3e87d" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(x=-2\)" data-solution-options='["\\(y=33\\)", "\\(y=-4\\)", "\\(x=3\\)", "\\(x=-2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<li>Line \(y - 3 = 0\)<br>
Point \((-2, -4)\) </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=-2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.14.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(x=-2\). </p>
<p>The slope of a line parallel to \(y −3 = 0\) is undefined. The line contains the point (−2,−4).<br>
The only equation with an undefined slope passing through (−2,−4) is \(x = −2\).</p>
</div>
</div>
<br>
<!--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>