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0e917220-f905-4ae0-a004-e827a916bab5.html
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<h4>Student Activity</h4>
<p>Now that you have written equations from tables, it is time to write systems of equations from graphs.</p>
<p><strong>Part 1: Writing a System of Equations from a Given Graph
</strong></p>
<p>For questions 1–8, use the given graph:</p>
<img src="https://k12.openstax.org/contents/raise/resources/b54289584768c0c3eff29af44751b7ab9f385f7a" width="300"><br>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="8ab13415-f850-440b-9ac1-7f67c5120a0f" 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="0a49b738-8436-497d-8638-18fa613b6ced" data-problem-comparator="integer" data-problem-type="input" data-solution="9">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li> For the green dashed line what is the \(y\)-value of the \(y\)-intercept? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 9</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 9.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#2-->
<div class="os-raise-ib-pset-problem" data-content-id="ec23dfc4-4e5e-4dfc-b5a8-854b9fbd123c" data-problem-comparator="float" data-problem-type="input" data-solution="-1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li> For the green dashed line what is the slope? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -1</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -1.</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>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="08cafc70-8ff8-430b-9db2-f00185f49b69" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> What is the equation of the green dashed line in slope-intercept 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>\(y= -x+9\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="52e20ed6-9d9c-484d-b3fc-5e99168f3ed6" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#4-->
<div class="os-raise-ib-pset-problem" data-content-id="adafd334-fdb7-43a1-aa7d-69c9835cde5a" data-problem-comparator="integer" data-problem-type="input" data-solution="5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li> For the orange solid line what is the \(y\)-value of the \(y\)-intercept? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 5.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="e5b6a568-4cef-49f8-a35b-df8ac3233ff4" data-problem-comparator="integer" data-problem-type="input" data-solution="3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li> For the orange solid line what is the slope? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 3.</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>
<br>
<!--Q#6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="051f37ba-13c3-49b7-9369-70acaddcc781" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li> What is the equation of the orange solid line in slope-intercept 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>\(y = 3x +5\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="295ce750-267f-4ad4-b1a6-e29b4ef0f370" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<li> Write the two equations as a system of linear equations. </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>\(y= -x+9\)</p>
<p>\(y = 3x +5\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dcd78e23-d9c8-4dbc-af9f-e8dad14e58da" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li> What is the solution of the system of equations? </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>\((1, 8)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<p><strong>Part 2: Use a Graph to Solve a Given System</strong></p>
<p>Now that you wrote a system of equations from a given graph, how can you work backward and graph a given system of equations by hand? Discuss this with a partner.</p>
<p>For questions 1 - 2, use this system of equations:</p>
<p>\(y=4x-4\)</p>
<p>\(y= -2x+8\)</p>
<br>
<!--Q#1-->
<ol class="os-raise-noindent">
<li> On the same coordinate plane, graph \(y = 4x -4\) and \(y = -2x +8\) by hand.
</li>
</ol>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!--QUESTION IS OUTSIDE OF INTERACTION DUE TO DESMOS-->
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then 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="Reveal1">
<p>Compare your answer:</p>
<img src="https://k12.openstax.org/contents/raise/resources/122a63c57e6341129b9a0bc2d23dbe6ed6a955a3" width="300"><br>
<br>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="568a4f5a-ea06-4630-9d55-8f0903374f0d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> What is the solution to the system of equations? </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>\((2, 4)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>For numbers 3 and 4, consider the system of equations:</p>
<p>\(y = - \frac{3}{4}x+5\)</p>
<p>\(y=\frac{1}{2}x-5\)</p>
<br>
<!--Q#3-->
<ol class="os-raise-noindent" start="3">
<li> On the same coordinate plane, graph the system of equations by hand. </li>
</ol>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!--QUESTION IS OUTSIDE OF INTERACTION DUE TO DESMOS-->
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then 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="Reveal3">
<p>Compare your answer:</p>
<img src="https://k12.openstax.org/contents/raise/resources/a4d952b331993f138b72346cb75349dcf901fc83" width="300"><br><br>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="6017b45b-087a-4018-9cd5-6cc3d1bb0ea0" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> What is the solution to the system of equations? </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>\((8, -1)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<h4>Video: Graphing a System of Equations</h4>
<p>Watch the following video to learn more about writing systems of equations from graphs.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/RQHhdqkJEo0?si=lGR1PpEOg-oREXv2;&rel=0" title="YouTube video player"></iframe></div>
</div>
<br>
<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>
<!--Start interaction. If multiple interactions appear under "are you ready for more?, they should all have matching "data-wait-for-event", which should also match the "data-fire-event" for the button. Note in this sample, they are all RFM1-->
<br>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e32ca634-67c4-45bc-aaec-d5e17b0ce4b4" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Graph the following system of equations on a coordinate plane:</p>
<p>\(y=2x +5\)</p>
<p>\(4x-2y =10\)</p>
<p>Find the solution.</p>
<p>(Hint: For the second equation, solve for \(y\) first.)</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:</p>
<p>Infinitely many solutions. When the second equation is solved for \(y\), it becomes \(-2y =-4x=10\) then \(y = 2x +5\). Both equations are the same. So, on the graph, one line is on top of the other and all solutions are possible.</p>
</div>
</div>
<!--End interaction-->