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<h4>Activity</h4>
<br>
<div class="os-raise-familysupport">
<p>Access the <a href="https://k12.openstax.org/contents/raise/resources/ad776e2f4b03a08bf69ddddc59a1efd31551b1a0" target="_blank">Desmos guide PDF</a> for tips on solving problems with the Desmos graphing calculator.</p>
</div>
<br>
<p>Use the following scenario for questions 1 - 5:<br>
A student has a savings account with $475 in it. She deposits $125 of her paycheck into the account every week. Her
goal is to save $7000 for college.
</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="81c33abc-0d93-4718-9a65-e8f3476c4188" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="ada32325-2724-477f-90a1-aa013e3a2f66" data-problem-comparator="integer" data-problem-type="input" data-solution="850">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>How much will be in the account after 3 weeks?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 850</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 850.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="2497e810-58d6-409f-ad78-5207d7fd06e0" data-problem-comparator="integer" data-problem-type="input" data-solution="7">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>How many weeks will it take until she has $1350?
</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 7</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 7.</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>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="042b1d00-55fd-483c-89a0-77a66a6babe9" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Write an equation that represents the relationship between the dollar amount in her account and the number of
weeks of saving.</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>\(a=475+125w\), where \(a\) is the dollar amount in the account and \(w\) is the number of
weeks of savings.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q4-->
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<br>
<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">
<ol class="os-raise-noindent" start="4">
<li>Graph your equation using graphing technology. Mark the points on the graph that represent the amount after 3
weeks and the week she has $1350. Write down the coordinates.
Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using
the Desmos tool above.
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>When 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="Reveal3">
<p>Compare your Answer:</p>
<img alt="Graph of a linear function. amount in account (dollars), number of weeks." height="194" src="https://k12.openstax.org/contents/raise/resources/fb79cc0520f9d5754497ccaff23da6041fa25ab4" width="251">
<br>
<br>
</div>
<!--Interaction End -->
<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-attempts-exhausted-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<!--Q#5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="966d218c-97ce-40d1-b04c-48c5ad5d9ab4" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>What is the \(x\)-intercept? </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>The correct answer is \((475, 0)\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5d4868ad-0366-414a-b9b6-c3fbd128ef06" 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 other information does the \(x\)-intercept identify in the function?</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: The \(x\)-intercept can identify the zero of the function since it represents where the function equals zero \((y = 0)\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="c5e37e2f-4c45-4dce-9517-df35744e024c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<li>What is the the \(y\)-intercept?</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>The correct answer is \((0, -3.8)\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="39454fa9-82e0-49e8-923c-84916f0f591d" 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 slope?</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>The correct answer is \(-\frac{1}{125}\).</p>
</div>
</div>
<!--Interaction End -->
<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-->
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dc13fa0d-e44e-4a42-922d-44b972932ee4" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<blockquote>
<p>Use the following information to answer questions 1 - 5. A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.</p>
</blockquote>
<ol class="os-raise-noindent">
<li>Write an equation that represents the relationship between the gallons of water in the tank and hours the tank
has
been draining.</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>\(a=450-1,200h\) where \(h\) is time in hours.</p>
</div>
</div>
<!--End interaction-->
<br>
<!--Q2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="17d69262-508b-4ef1-bfec-289106ef7928" 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>Write an equation that represents the relationship between the gallons of water in the tank and seconds the
tank
has been draining.</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>\(a=450-\frac{s}{3}\) where \(s\) is time in seconds.</p>
</div>
</div>
<!--End interaction-->
<br>
<!--Q3 new-->
<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="ba4fcd2f-c89e-499d-a82c-07b051c2bbcd" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Graph each of your new equations.<br>Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the Desmos tool above. </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>
<img alt="Linear function." height="195" src="https://k12.openstax.org/contents/raise/resources/54873f473fb892340f99aa047fc492c3531f2c16" width="245">
<br>
<br>
</div>
</div>
<!--End interaction-->
<br>
<!--Q4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4eaf6ba6-7054-4c72-9179-90b784109fff" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>In what way are all of the graphs the same? In what way are they all different? Write down your answer. </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>Your answer may vary, but here are some samples. </p>
<ul>
<li>They all have the same \(y\)-intercept.
</li>
<li>They all decrease.
</li>
<li>The slopes are different.
</li>
</ul>
</div>
</div>
<!--End interaction-->
<br>
<!--Q5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="91e6901f-f2bc-4738-997a-e3bf1fa8a27d" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>How would these graphs change if we used quarts of water instead of gallons? What would stay the same?</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>Your answer may vary, but here are some sample samples:<br>
The graphs would still be lines with negative slopes that are different. They would have the same horizontal intercepts. The vertical intercepts would be different, but they would represent the same amount of water.
</p>
</div>
</div>
<!--End interaction-->
<br>