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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<p>For numbers 1–2, use the graph below:</p>
<img alt="This figure a shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The line goes through the points (negative 6, negative 8), (negative 4, negative 6), (negative 2, negative 4), (0, negative 2), (2, 0), (4, 2), (6, 4), (8, 6)." src="https://k12.openstax.org/contents/raise/resources/b43d81b1ae710bc8b78c0278758a16ed71d489d9"><br>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="0a202dbf-bfda-49f2-bdb0-f78c50c533fd" 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="183419ea-c11a-4339-aadb-d9f6fddd56ed" data-problem-type="dropdown" data-retry-limit="3" data-solution="(2,0)" data-solution-options='["(0,2)", "(2,0)", "(0,-2)", "(-2,0)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>What are the coordinates of the \(x\)-intercept of the graph?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph crosses the \(x\)-axis at \((0,2)\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((2,0)\). </p>
</div>
</div>
<br>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="0ff195d9-131c-40b6-9d54-694f267a6025" data-problem-type="dropdown" data-retry-limit="3" data-solution="(0,-2)" data-solution-options='["(0,2)", "(2,0)", "(0,-2)", "(-2,0)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>What are the coordinates of the \(y\)-intercept of the graph?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph crosses the \(y\)-axis at \((0,-2)\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((0,-2)\). </p>
</div>
</div>
<br>
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="328040c7-4577-4c54-ba53-f3023e8a8ae7" data-problem-type="dropdown" data-retry-limit="3" data-solution="(3,0)" data-solution-options='["(0,2)", "(2,0)", "(0,3)", "(3,0)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For numbers 3–4, use the graph below:</p>
<img alt="This figure a shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The line goes through the points (negative 6, 6), (negative 3, 4), (0, 2), (3, 0), (6, negative 2), and (9, negative 4)." src="https://k12.openstax.org/contents/raise/resources/7825f9d07108bf3c79a1b240974ac6f172bdfca7"> <br>
<br>
<ol class="os-raise-noindent" start="3">
<li>What are the coordinates of the \(x\)-intercept of the graph?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph crosses the \(x\)-axis at (3,0).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The graph crosses the \(x\)-axis at \((3,0)\). </p>
</div>
</div>
<br>
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="d9f6c4de-fe6a-4f3e-8663-849afb187a67" data-problem-type="dropdown" data-retry-limit="3" data-solution="(0,2)" data-solution-options='["(0,2)", "(2,0)", "(0,-2)", "(-2,0)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>What are the coordinates of the \(y\)-intercept of the graph?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph crosses the \(y\)-axis at \((0,2)\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((0,2)\). </p>
</div>
</div>
<br>
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="3adaa38d-78ca-4063-bee4-3133a26edf43" data-problem-type="dropdown" data-retry-limit="3" data-solution="(4,0)" data-solution-options='["(0,12)", "(12,0)", "(4,0)", "(0,4)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>What are the coordinates of the \(x\)-intercept of the equation \(3x + y = 12\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(y = 0, 3x + 0 = 12\) becomes \(x = 4\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((4,0)\). </p>
</div>
</div>
<br>
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="99318492-7d7c-491b-b4ea-a460dfe1073b" data-problem-type="dropdown" data-retry-limit="3" data-solution="(0,12)" data-solution-options='["(0,12)", "(12,0)", "(4,0)", "(0,4)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li>What are the coordinates of the \(y\)-intercept of the equation \(3x + y = 12\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! When \(x = 0, 3(0) + y = 12\) becomes \(y = 12\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((0,12)\). </p>
</div>
</div>
<br>
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="b15f1dc1-aa05-4cbf-b354-2c2c6129903f" data-problem-comparator="math" data-problem-type="input" data-solution="\frac{3}{2}">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>What is the slope of the line \(3x- 2y=6\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The slope is \(\frac{3}{2}\), calculated from the equation in standard form.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Remember the formula for slope in standard form. Use the Equation Editor to express your answer.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(\frac{3}{2}\). The slope is found by rearranging the equation into slope-intercept form and identifying the coefficient of \(x\).</p>
</div>
</div>
<br>
<!--Q8-->
<div class="os-raise-ib-pset-problem" data-content-id="8179854f-8533-4972-b9f9-094d93ae10f2" data-problem-comparator="integer" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>What is the \(y\)-intercept of \(y = 6x + 2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Compare your answer:<br>
In \(y = mx + b\), the \(b\) is the \(y\)-intercept. In this equation, \(b = 2\).
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((0, 2)\). In \(y = mx + b\), the \(b\) is the \(y\)-intercept. In this equation, \(b = 2\). </p>
</div>
</div>
<br>
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="fcec07ea-a807-4295-af28-e0b61a16035d" data-problem-comparator="integer" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>What is the \(y\)-intercept of \(10x + 5y = 30\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Compare your answer:<br>
Solve for \(y\).<br>
\(10x - 10x + 5y = 30 - 10x\)<br>
\(5y = -10x + 30\)<br>\(\frac{5y}{5}=\frac{-10x +30}{5}\)<br>
\(y = -2x + 6\)<br>
In \(y = mx + b\), the \(b\) is the \(y\)-intercept. In this equation, \(b = 6\).
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((0, 6)\). <br>Solve for \(y\).<br>
\(10x - 10x + 5y = 30 - 10x\)<br>
\(5y = -10x + 30\)<br>\(\frac{5y}{5}=\frac{-10x +30}{5}\)<br>
\(y = -2x + 6\)<br>
In \(y = mx + b\), the \(b\) is the \(y\)-intercept. In this equation, \(b = 6\). </p>
</div>
</div>
<br>
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="5c1e1577-2cff-4350-8771-d6abb4e818c3" data-problem-type="multiplechoice" data-retry-limit="2" data-solution="a" data-solution-options='["a", "b", "c"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<li>Which graph represents the equation \( 12=3x+4y \)? Explain how you know.</li>
</ol>
<ol type="a">
<li><br>
<img alt height="238" role="presentation" src="https://k12.openstax.org/contents/raise/resources/a6168a6019660ea9b265ba1bac0348b9b39141e2" width="238">
</li>
<li><br>
<img alt class="img-fluid atto_image_button_text-bottom" height="238" role="presentation" src="https://k12.openstax.org/contents/raise/resources/3505fd868a59a904a12adbf1667c928455c2ebcd" width="238">
</li>
<li><br>
<img alt height="238" role="presentation" src="https://k12.openstax.org/contents/raise/resources/2a2eb8b183db689ad120aa6b36d0452cbbd0dfcf" width="238">
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Graph a, because the intercepts are \((4, 0)\) and \((0,3)\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 1.11.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is Graph \(a\), because the intercepts are \((4, 0)\) and \((0,3)\). </p>
<p>When \(x = 0\), \(12 = 3(0) + 4y\) gives \(y = 3\). The \(y\)-intercept is at (0, 3). When \(y = 0\), \(12 = 3x + 4(0)\) gives \(x = 4\). The \(x\)-intercept is (4, 0). Graph \(a\) has these intercepts.</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>