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2ee912c9-51d1-4dcd-b32c-0efa0fdcf7b5.html
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<h4>Activity</h4>
<p>For numbers 1–5, select the slope and intercept that corresponds to each equation:</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="ddc8cc1b-4b5c-4970-bde1-f2ae532c4819" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#1-->
<div class="os-raise-ib-pset-problem" data-content-id="6c21e788-9cde-4e5b-94cc-e15e1e947b3f" data-problem-type="multiplechoice" data-solution="\( m=\frac 43 \), \( y\text{-int}=(0,1) \)" data-solution-options='["\\( m=3 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,-2) \\)", "\\( m=-4 \\), \\( y\\text{-int}=(0,8) \\)", "\\( m=3 \\), \\( y\\text{-int}=(0,-2) \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>\( -4x+3y=3 \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( m=\frac 43 \), \( y\text{-int}=(0,1) \)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \( m=\frac 43 \), \( y\text{-int}=(0,1) \)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#2-->
<div class="os-raise-ib-pset-problem" data-content-id="290e6cf0-44ff-4e9c-88f4-1105c2b6945d" data-problem-type="multiplechoice" data-solution="\( m=3 \), \( y\text{-int}=(0,-2) \)" data-solution-options='["\\( m=3 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,-2) \\)", "\\( m=-4 \\), \\( y\\text{-int}=(0,8) \\)", "\\( m=3 \\), \\( y\\text{-int}=(0,-2) \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>\( 12x-4y=8 \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( m=3 \), \( y\text{-int}=(0,-2) \)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \( m=3 \), \( y\text{-int}=(0,-2) \)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#3-->
<div class="os-raise-ib-pset-problem" data-content-id="dc16004d-1b6c-4990-830a-3a35112e31e5" data-problem-type="multiplechoice" data-solution="\( m=-4 \), \( y\text{-int}=(0,8) \)" data-solution-options='["\\( m=3 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,-2) \\)", "\\( m=-4 \\), \\( y\\text{-int}=(0,8) \\)", "\\( m=3 \\), \\( y\\text{-int}=(0,-2) \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>\( 8x+2y=16 \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( m=-4 \), \( y\text{-int}=(0,8) \)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \( m=-4 \), \( y\text{-int}=(0,8) \)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#4-->
<div class="os-raise-ib-pset-problem" data-content-id="85f7342e-2dc9-4623-b35e-32e5737b516d" data-problem-type="multiplechoice" data-solution="\( m=3, y\text{-int}=(0,1) \)" data-solution-options='["\\( m=3, y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,-2) \\)", "\\( m=-4 \\), \\( y\\text{-int}=(0,8) \\)", "\\( m=3 \\), \\( y\\text{-int}=(0,-2) \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>\( -x+\frac 13 y=\frac 13 \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! ( m=3 \), \( y\text{-int}=(0,1) \)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \( m=3 \), \( y\text{-int}=(0,1) \)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="4f72d334-bc7f-4d5d-bf3e-1696a83110e9" data-problem-type="multiplechoice" data-solution="\( m=\frac 43 \), \( y\text{-int}=(0,-2) \)" data-solution-options='["\\( m=3 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,1) \\)", "\\( m=\\frac 43 \\), \\( y\\text{-int}=(0,-2) \\)", "\\( m=-4 \\), \\( y\\text{-int}=(0,8) \\)", "\\( m=3 \\), \\( y\\text{-int}=(0,-2) \\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>\( -4x + 3y = -6 \)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( m=\frac 43 \), \( y\text{-int}=(0,-2) \)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \( m=\frac 43 \), \( y\text{-int}=(0,-2) \)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
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</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
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</div></div>
<br>
<p><strong>Using Standard Form and Intercepts to Graph</strong></p>
<p> Standard form, \(Ax + By = C\), is helpful for finding the \(x\)-intercepts and \(y\)-intercepts of an equation. </p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="943d7507-2a41-427c-b862-a04006a2eb93" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#6-->
<div class="os-raise-ib-pset-problem" data-content-id="d693b658-f7c3-4288-9f1b-0baf9a491166" data-problem-comparator="integer" data-problem-type="input" data-solution="0">
<div class="os-raise-ib-pset-problem-content">
<p> For questions 6-11, </p>
<blockquote>Use the equation \(6x -4y=24\).</blockquote>
<ol class="os-raise-noindent" start="6">
<li>What is the value of \(y\) at the \(x\)-intercept?</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 0</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 0.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#7-->
<div class="os-raise-ib-pset-problem" data-content-id="8bab532e-ecf3-48f9-a6e5-4505f13ce64e" data-problem-comparator="integer" data-problem-type="input" data-solution="4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>What is the \(x\)-intercept of the equation?</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 4</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 4.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#8-->
<div class="os-raise-ib-pset-problem" data-content-id="04605dc6-d8fc-45b1-a167-4208032018fe" data-problem-comparator="integer" data-problem-type="input" data-solution="4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>What is the value of \(x\) at the \(y\)-intercept?</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 0</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 0.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#9-->
<div class="os-raise-ib-pset-problem" data-content-id="59849d8c-16fa-497f-85ed-a7fc1d68615a" data-problem-comparator="integer" data-problem-type="input" data-solution="4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>What is the \(y\)-intercept of the equation?</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -6</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is -6.</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-attempts-exhausted-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div></div>
<!--BEGIN ADD DESMOS INTERATIVE-->
<!--START QUESTION #10 -->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal55" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
<ol class="os-raise-noindent" start="10">
<li>Use the graphing tool or technology outside the course. Plot the two intercepts and the equation of the line, using the Desmos tool below.
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>After you have finished graphing, select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal55">
<p>Compare your answer:</p>
<!--REPLACE IMAGE BELOW WITH CORRECT IMAGE-->
<img alt="Plot of two intercepts, four comma zero and zero comma negative six for the equation of the line." src="https://k12.openstax.org/contents/raise/resources/9054a198ed1dd108b3ab9e20c689b592f412a08e" width="400">
<br>
<br>
</div>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<!--END ADD DESMOS INTERATIVE-->
<!--Q#11-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9f1f9c57-2039-42e0-8a11-23a38055a97c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="11">
<li>Using the graph from question 10, what is the slope of the line in simplest form?</li>
</ol>
</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:</p>
<p> \(\frac32\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="12550256-65fa-4989-9565-6a8f2bae93fe" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>For numbers 1-2, use the equations below:</p>
<blockquote>
<p>These are the equations from the activity. Each equation is in the form \(Ax+By=C\)</p>
</blockquote>
<p>\( 4x - 3y = -3 \)<br>
\( 12x - 4y = 8 \)<br>
\( 8x + 2y = 16 \)<br>
\( 3x - y = -1\)<br>
\( 4x - 3y = 6 \)
</p>
<ol class="os-raise-noindent">
<li>Observe the graph of the equation \(−4x+3y=3\) where it is graphed, on the same coordinate plane, with another line passing through \((0,0)\) and \((A,B)\). In this example \(A=-4\) and \(B=3\), so the other line would pass through \((0,0)\) and \((−4,3)\). What do you notice about the lines?
</li>
</ol>
</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:</p>
<p>Answers may vary, but here is a sample.<br>The two lines are perpendicular.
</p>
<p><img src="https://k12.openstax.org/contents/raise/resources/d6be84743f72a71b97f9a7e1e00e6c0529fc3a3b" width="300"></p>
</div>
</div>
<br>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0" data-wait-for-event="RFM1"></div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3b5338fd-116a-4954-92ee-c183a5a9b4f3" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the Desmos tool above. Then make another observation about the lines.</li>
</ol>
</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:</p>
<p>Answers may vary, but here is a sample.The two lines are always perpendicular.</p>
<p><img src="https://k12.openstax.org/contents/raise/resources/d6be84743f72a71b97f9a7e1e00e6c0529fc3a3b" width="300"></p>
</div>
</div>