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<h4>Activity</h4>
<p>For this activity, you will use two graphs that represent situations you saw in other activities. </p>
<p>For questions 1–3, use the graph below:<br>
The graph represents \(a = 450 − 20t\), which describes the relationship between gallons of water in a tank and time
in minutes.</p>
<img alt="Graph of a line. Vertical axis, amount in tank, gallons. Horizontal axis, time, minutes." height="195" src="https://k12.openstax.org/contents/raise/resources/627ff6c21d4900907647e8abc921dfb1111f374a" width="244"><br>
<br>
<br>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="73e99da6-e753-4d56-a66c-f0e6e834377a" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Where on the graph can we see the 450?</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> 450 is where the graph intersects the
vertical axis.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="543c8ae7-a378-4cfe-a990-61d000f5638f" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Where can we see the -20? </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> −20 is the slope.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ba0f1c77-7a49-4fc2-bb0b-cd3fe8e40793" 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 do the numbers 450 and -20 mean in the situation that is graphed?</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 is a sample. <br>
450 is the gallons of water in the tank at 0 minutes, before the tank starts to be drained. −20
means the gallons of water (vertical value) drops by 20 for every 1 minute increase in time (horizontal value).
</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="f9b967f2-1d01-4c29-81a9-dc196c6225ab" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> The graph represents \(6x +9y = 75\). It describes the relationship between pounds of almonds and figs and the
dollar amount Clare spent on them. Suppose a classmate says, “I am not sure the graph represents \(6x +9y = 75\)
because I don’t see the 6, 9, or 75 on the graph.” How would you show your classmate that the graph indeed
represents this equation? <br>
<br>
<img alt="Graph of a line. Vertical axis, dried figs, pounds. Horizontal axis, Almonds, pounds." height="196" src="https://k12.openstax.org/contents/raise/resources/e183cfb486b4c8793f50d9d287a0c65abc863bad" width="239">
</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 is a sample.</p>
<ul>
<li> If we substitute 0 for \(x\) in the equation and solve for \(y\), we get \(\frac {75}{9}\) or \(8 \frac 13\) . That combination is the point
\((0,8 \frac 13)\) or the \(y\)-intercept of the graph. If we substitute 0 for \(y\) in the equation and solve for \(x\), we
get 12.5 for \(x\). That combination is the point (12.5,0) or the \(x\)-intercept of the graph.</li>
<li>If we substitute the \(x\)- and \(y\)-values of any point on the graph in the equation, the equation remains true.</li>
<li>If we rewrite the equation and solve for \(y\), we have \( y = \dfrac {75 - 6x}{9} \) or \( y = 8\frac13 - \frac23x \). The \( 8\frac13 \) matches where the graph
intersects the \(y\)-axis and \( -\frac23\) matches the slope of the
graph. (For every 3 additional pounds of almonds that Clare bought, she could buy 2 fewer pounds of figs.)</li>
<li>From the graph, we can see that the \(y\)-intercept is \( (0,8\frac13) \) and the slope is \( -\frac23 \), so the equation of the line is
\( y = 8\frac13 - \frac23x \). Multiplying each side of the equation by 9 (an acceptable move) gives an equivalent equation, \( 9y = 75 - 6x\),
which can be rewritten as \( 6x + 9y = 75\).</li>
</ul>
</div>
</div>
<!--Interaction End -->