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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<p>(Technology required.)</p>
<p>Use graphing technology to create a scatter plot and find the best fit line.</p>
<ol class="os-raise-noindent">
<li>What does the best fit line estimate for the \(y\)-value when \(x\) is 100?</li>
</ol>
<br>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="910ee686-c1fa-4767-8b57-cd58cdfcb4a0" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="2213c4f6-63a8-43f1-88d4-65cbbcb95f2b" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="125" data-solution-options='["100", "125", "150", "120"]'>
<div class="os-raise-ib-pset-problem-content">
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col"> \(x\) </th>
<th scope="col"> \(y\) </th>
</tr>
</thead>
<tbody>
<tr>
<td> 83 </td>
<td> 102 </td>
</tr>
<tr>
<td> 87 </td>
<td> 115 </td>
</tr>
<tr>
<td> 91 </td>
<td> 107 </td>
</tr>
<tr>
<td> 93 </td>
<td> 122 </td>
</tr>
<tr>
<td> 97 </td>
<td> 125 </td>
</tr>
<tr>
<td> 97 </td>
<td> 127 </td>
</tr>
<tr>
<td> 101 </td>
<td> 120 </td>
</tr>
<tr>
<td> 104 </td>
<td> 127 </td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The line of best fit is \(y=1.089x+15.588\), so when \(x\) is 100, \(y\) is about 125.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 3.2.2–3.23.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer for the line of best fit is \(y=1.089x+15.588\), so when \(x\) is 100, \(y\) is about 125. <br>
</p>
</div>
</div>
<!--END QUESTION.-->
<br>
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="c769c078-adf6-4f2f-bd88-1986cf4d4423" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="The slope is 0.404, which means for every day, the plant grows 0.404 centimeters. " data-solution-options='["The slope is 5.18, which means for every day, the plant grows 5.18 centimeters.", "The slope is 0.404, which means for every day, the plant grows 0.404 centimeters. ", "The slope is -5.18, which means for every day, the plant shrinks -5.18 centimeters. ", "The slope is 0.404, which means the plant grows 1 centimeter every 0.404 days."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>A seed is planted in a glass pot, and its height is measured in centimeters every day.</li>
</ol>
<img alt="A scatter plot. Horizontal, 0 to 30, by 1’s, labeled days. Vertical, negative 5 to 3, by point 5’s, labeled height in centimeters. 21 dots trend linearly up and to the right with a line a best fit." src="https://k12.openstax.org/contents/raise/resources/81da6887d175f5dd827e61bafa3f8293c749e3ad"><br>
<br>
<p>The best fit line is given by the equation \(y=0.404x−5.18\), where \(y\) represents the height of the
plant above ground level, and \(x\) represents the number of days since it was planted.</p>
<p>What is the slope of the best fit line? What does the slope of the line mean in this situation? </p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The slope is 0.404, which means for every day, the plant grows 0.404 centimeters. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 3.2.2–3.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: The slope is 0.404, which means for every day, the plant grows 0.404 centimeters. </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>
<p>Use the following information to answer questions 3 - 5. </p>
<blockquote>
<p>The scatter plots below show different lines that students used to model the relationship between body mass
(in pounds) and bite force (in pounds) for crocodiles.</p>
<p>Match each graph to one of the equations below, and explain your reasoning. Let \(B\) represent bite force (in
pounds) and \(W\) represent body mass (in pounds).</p>
<div class="os-raise-d-flex os-raise-justify-content-between"> <img alt="A SCATTER PLOT THAT SHOWS BODY MASS IN POUNDS ON THE X-AXIS AND BITE FORCE IN POUNDS ON THE Y-AXIS. THE LINE DRAWN INCREASES FROM LEFT TO RIGHT AND HAS A \(y\)-intercepts BETWEEN 200 AND 300." height="178" src="https://k12.openstax.org/contents/raise/resources/c769c50c5d9a7152b372e98b073c7dae2e860b1e" width="200"> <img alt="A SCATTER PLOT THAT SHOWS BODY MASS IN POUNDS ON THE X-AXIS AND BITE FORCE IN POUNDS ON THE Y-AXIS. THE LINE DRAWN INCREASES FROM LEFT TO RIGHT AND HAS A \(y\)-intercepts BETWEEN 300 AND 400.
" height="184" src="https://k12.openstax.org/contents/raise/resources/f2db925d3b7a849e49e2bbb5aa9bb13ad030fea9" width="200"> <img alt="A SCATTER PLOT THAT SHOWS BODY MASS IN POUNDS ON THE X-AXIS AND BITE FORCE IN POUNDS ON THE Y-AXIS. THE LINE DRAWN INCREASES FROM LEFT TO RIGHT AND HAS A \(y\)-intercepts BETWEEN 100 AND 200. " height="184" src="https://k12.openstax.org/contents/raise/resources/82f0c78f8c372c36c200f5481057789b8ce87014" width="200"></div>
</blockquote>
<br>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="b976af83-e1fc-4129-895d-f62bf72086a9" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="2a497ced-dbcd-445e-ac8d-01255b47f460" data-problem-type="dropdown" data-retry-limit="2" data-solution="Line 3" data-solution-options='["Line 1", "Line 2", "Line 3"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Which graph represents data that could be modeled by the equation,
\(B = 3.28W + 126\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Line 3 and Equation 1 match because the intercept of Equation 1 is the smallest, which seems to match
the graph. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 3.2.1.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: Line 3 and Equation 1 match because the intercept of Equation 1 is the smallest, which
seems to match the graph. </p>
</div>
</div>
<!--END QUESTION.-->
<!--Q3b-->
<div class="os-raise-ib-pset-problem" data-content-id="7c1ce9c3-b22a-497d-b5f0-292bb5e4b48a" data-problem-type="dropdown" data-retry-limit="2" data-solution="Line 2" data-solution-options='["Line 1", "Line 2", "Line 3"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>Which graph represents data that could be modeled by the equation,
\(B = 3.04W + 351\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Line 2 and Equation 2 match because the intercept of Equation 2 is larger, so it matches Line 2, which
has a \(y\)-intercept closer to 400.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 3.2.1.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: Line 2 and Equation 2 match because the intercept of Equation 2 is larger, so it matches
Line 2, which has a \(y\)-intercept closer to 400. </p>
</div>
</div>
<!--END QUESTION.-->
<br>
<!--Q3b-->
<div class="os-raise-ib-pset-problem" data-content-id="970607b5-89fc-4744-8890-a013a6d9f3fa" data-problem-type="dropdown" data-retry-limit="2" data-solution="Line 1" data-solution-options='["Line 1", "Line 2", "Line 3"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Which graph represents data that could be modeled by the equation,
\(B = 2.16W + 267\)? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Line 1 and Equation 3 match because the intercept of 267 appears to match the graph, which has
the second-largest intercept.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 3.2.1.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: Line 1 and Equation 3 match because the intercept of 267 appears to match the graph,
which has the second-largest intercept. </p>
</div>
</div>
<!--END QUESTION.-->
<br>
<!--Q#6new-->
<div class="os-raise-ib-pset-problem" data-content-id="f2e32e15-3966-494b-b130-e03c979a9bfe" data-problem-type="multiplechoice" data-solution="\(Y=6x\)" data-solution-options='["\\(Y=6x\\)", "\\(Y=6x+6\\)", "\\(Y=\\frac16x\\)", "\\(Y=\\frac16x+6\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li>Mike owns a grass cutting business. The table below shows how many yards, \(Y\), he can cut in \(x\) days.</li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row">Number of days, x</th>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
</tr>
<tr>
<th scope="row">Number of yards cut, Y</th>
<td>6</td>
<td>12</td>
<td>18</td>
<td>24</td>
</tr>
</tbody>
</table>
<br>
<p>Which of the following equations is a linear model representing the number of yards, \(Y\), Mike can cut in \(x\) days.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(Y =6d\)</p>
<p>Since the change in \(y\) is 6 and change in \(x\) is 1, the slope is 6. Working backwards, when \(x = 0\), \(Y=0\) so the equation becomes \(Y=6x+0\) or \(Y = 6x\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 3.2.3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(Y = 6x\)</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>