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<h4>Activity</h4>
<p>Use the following information to answer questions 1 - 4. </p>
<blockquote>
The graph of \(f(x) = 2x + 6\) is graphed below. Answer the questions about the linear function and its key features.
</blockquote>
<p><img alt="GRAPH OF A LINE WITH AN \(x\)-intercepts OF −3 AND \(y\)-intercepts OF 6." height="297" src="https://k12.openstax.org/contents/raise/resources/883d5444bd5bb58e4fd98f9e360dd63cace83db2" width="300"></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8da6c903-b5d4-47f6-aa27-c9b7c7dd5403" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="1">
<li>What is the value of \(f(-3)\)?</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>0</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="c9f71c3f-a879-4f1c-8dd3-5178afc1d907" 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 key feature of the linear function is the point \((-3,0)\)?</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 \(x\)-intercept, or zero</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4bf1cd63-93b8-4312-aeda-953889d52d4c" 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 slope of the linear 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:</p>
<p>2</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4cdccca7-0637-4d26-88cb-d94b1999b411" 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 part of the linear function is the point \((0, 6)\)?</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 \(y\)-intercepts
</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>Use the following information to answer questions 5 - 8. </p>
<blockquote>
The amount of money Adam saves in dollars is shown in the graph below.
</blockquote>
<img alt="GRAPH THAT SHOWS THE TOTAL AMOUNT OF MONEY IN DOLLARS AS A FUNCTION OF NUMBER OF DAYS. THE FUNCTION IS A LINE WITH A POSITIVE SLOPE THAT PASSES THROUGH THE POINTS (0, 3) AND (1, 6)." height="301" src="https://k12.openstax.org/contents/raise/resources/a963f822c76db76cac7225e978193e50fed19143" width="300">
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="55503569-fca1-4903-b4e8-9c7c12dd0dce" 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 \(y\)-intercept of the graph?</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 point is \((0,3)\).
</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d43d819f-b019-4589-be3d-c11d381646e7" 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 does the \(y\)-intercepts mean in the context of the problem</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: Your answer may vary.</p>
<p>When Adam started saving, he already had 3 dollars on
day 0.
</p>
</div>
</div>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5ee7546d-55c3-42e5-945c-d55816412fce" 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 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 slope is 3.
</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1e09387e-f2b1-4f13-872a-9a7921ac40b3" 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 does the slope mean in the context of the problem</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: Your answer may vary.</p>
<p>Every 1 day, Adam saves 3 dollars.
</p>
</div>
</div>
<p>Use the following information to answer questions 9 - 12.</p>
<blockquote>The graph of \(f(x) = 13x + 2\) is graphed below. Identify the appropriate label for each key feature of the graph.</blockquote>
<p><img height="300" src="https://k12.openstax.org/contents/raise/resources/4de93ead19af6557e95474c5ea621808fdf1b873"></p>
<br>
<!--Q3a-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9587ebe5-0762-4350-9c46-94e944cea919" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="9">
<li>What is the key feature labeled \(A\) on the graph?
</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>\(A\), (0, 2), is the \(y\)-intercept.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q3b-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="220d4ed9-6f48-4972-ac59-d5a6ad3e823e" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="10">
<li>What is the key feature labeled \(B\) on the graph?
</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>\(B\), (-6, 0), is the \(x\)-intercept or zero.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q3c-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b2953d5d-7e7d-4b44-9fb4-3378ae6189ca" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="11">
<li>What is the key feature labeled \(C\) on the graph?
</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>\(C\), (0, 0), is the origin.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q3d-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1ee078c9-31d5-44b4-bde8-8028ecd693cf" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="12">
<li>What is the key feature labeled \(D\) on the graph?</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>\(D\), \(\frac13\), is the slope.</p>
</div>
</div>
<!--Interaction End -->
<br>