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a2424502-8f9a-47f7-a7c3-400c3d86cc23.html
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<h4>Activity</h4>
<p>Here are several scatter plots.</p>
<p>Use scatter plot A to answer questions 1 - 2.</p>
<img alt="Scatter plot with line of best fit." src="https://k12.openstax.org/contents/raise/resources/7886c10b5deddc1db19e2b428ec022d7aeebcb43"><br>
<br>
<br>
<p class="os-raise-indent">Scatter plot A: \( y = −9.25x + 400\)</p>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="f8293cb0-bffb-4b46-b08a-742f0eafc010" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> Using the horizontal axis for \(x\) and the vertical axis for \(y\), interpret the slope of the linear model in the situation shown. </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, but here is a sample.</p>
<p> For every increase in age of one year, the linear model estimates that the reaction time decreases by about 9.25 milliseconds.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="db387949-b62c-454c-ab9f-331dbb5b0560" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> If the linear relationship continues to hold for the situation, interpret the \(y\)-intercept of the linear model. </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, but here is a sample. </p>
<p> The reaction time estimated by the linear model for a newborn is 400 milliseconds.</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>Use scatter plot B to answer questions 3 and 4.</p>
<p class="os-raise-indent">Scatter plot B: \(y = 0.44x + 0.04\)</p>
<img alt="Scatterplot with line of best fit." src="https://k12.openstax.org/contents/raise/resources/ddcfeeab93ae517fc62e6dcbd7bbd03154b8f88f"><br>
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="f6fd2b79-02e0-46ac-9d44-069a63dcc496" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> Using the horizontal axis for \(x\) and the vertical axis for \(y\), interpret the slope of the linear model in the situation shown. </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, but here is a sample. </p>
<p> For every additional banana, the linear model estimates that the price increases by about $0.44.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5fcac4ab-3400-4d03-8b0f-e56b0c1f806f" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> If the linear relationship continues to hold for the situation, interpret the \(y\)-intercept of the linear model. </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, but here is a sample. </p>
<p> The price estimated by the linear model for purchasing zero bananas is $0.04.</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>Use scatter plot C to answer questions 5 - 6.</p>
<p class="os-raise-indent">Scatter plot C: \(y = 4x + 87\)</p>
<img alt="Scatter plot with line of best fit." src="https://k12.openstax.org/contents/raise/resources/64993998789d00281800519379a861ae9e11fa1e"><br>
<br>
<br>
<!--Q#5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dfead69c-ee8c-4bd2-ae97-d8fd93f8eca3" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li> Using the horizontal axis for \(x\) and the vertical axis for \(y\), interpret the slope of the linear model in the situation shown. </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, but here is a sample. </p>
<p> For each additional square foot, the linear model estimates that the cost to install flooring increases by about $4.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="c0e10353-3345-4561-8329-aa78de450db1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li> If the linear relationship continues to hold for the situation, interpret the \(y\)-intercept of the linear model. </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, but here is a sample. </p>
<p> The fixed cost to install flooring is $87.</p>
</div>
</div>
<!--Interaction End -->
<br>
<p class="os-raise-indent">Use scatter plot D to answer questions 7 and 8.</p>
<p>Scatter plot D: \(y = −2.4x + 25.0\)</p>
<img alt="Scatter plot with line of best fit." src="https://k12.openstax.org/contents/raise/resources/153ae4a39a9776291b8c8151ad6cac8fd7815a90"><br>
<br>
<br>
<!--Q#7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="011fb2e0-9bf0-4612-99fd-e25d397f4e39" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<li> Using the horizontal axis for \(x\) and the vertical axis for \(y\), interpret the slope of the linear model in the situation shown. </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, but here is a sample. </p>
<p> For every increase in temperature of 1 degree Celsius, the linear model estimates that the volume decreases by about 2.4 cubic centimeters.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a96cee2c-3764-403c-a8c5-7b34d7500e95" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li> If the linear relationship continues to hold for the situation, interpret the \(y\)-intercept of the linear model. </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, but here is a sample. </p>
<p>25 cubic centimeters is the volume estimated by the linear model for a temperature of zero degrees Celsius. </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-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="87b410d7-5592-4d7e-baf4-bed2ec17aa23" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Clare, Diego, and Elena collect data on the mass and fuel economy of cars at different dealerships. </p>
<p>Clare finds the line of best fit for data she collected for 12 used cars at a used car dealership. The line of best fit is \(y=\frac{-9}{1,000}x+34.3\) where \(x\) is the car’s mass, in kilograms, and \(y\) is the fuel economy, in miles per gallon.</p>
<p>Diego made a scatter plot for the data he collected for 10 new cars at a different dealership.</p>
<p><img alt="A scatter plot." src="https://k12.openstax.org/contents/raise/resources/8c8297915c59723742439e044d461048110e311e"></p>
<br>
<p>Elena made a table for data she collected on 11 hybrid cars at another dealership.</p>
<table class="os-raise-skinnytable">
<thead>
<tr>
<th scope="col"> mass (kilograms) </th>
<th scope="col"> fuel economy (miles per gallon) </th>
</tr>
</thead>
<tbody>
<tr>
<td> 1,100 </td>
<td> 38 </td>
</tr>
<tr>
<td> 1,200 </td>
<td> 39 </td>
</tr>
<tr>
<td> 1,250 </td>
<td> 35 </td>
</tr>
<tr>
<td> 1,300 </td>
<td> 36 </td>
</tr>
<tr>
<td> 1,400 </td>
<td> 31 </td>
</tr>
<tr>
<td> 1,600 </td>
<td> 27 </td>
</tr>
<tr>
<td> 1,650 </td>
<td> 28 </td>
</tr>
</tbody>
</table>
<br>
<ol class="os-raise-noindent">
<li>Interpret the slope and \(y\)-intercept of Clare’s line of best fit in this situation.</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 means that the fuel economy decreases 9 miles per gallon for every 1,000 kg increase in mass. The \(y\)-intercept represents the fuel economy of a car, in miles per gallon, that has a mass of 0 kg.</p>
</div>
</div>
<!--End interaction-->
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4ac9f67f-6509-4396-8493-31a1c05d7cfd" 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>Diego looks at the data for new cars and used cars. He claims that the fuel economy of new cars decreases as the mass increases. He also claims that the fuel economy of used cars increases as the mass increases. Do you agree with Diego’s claims? Be prepared to show your reasoning.</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> Diego’s claim about new cars is correct. You can look at the graph and see that the fuel economy tends to decrease as the mass increases because the scatter plot appears to have a negative slope. Diego’s claim about used cars is not correct because the line of best fit has a negative slope, which means that the fuel economy decreases as the mass increases.</p>
</div>
</div>
<!--End interaction-->
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="78442612-9e47-46fd-a64f-c6eaa746a4bb" 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>Elena looks at the data for hybrid cars and correctly claims that the fuel economy decreases as the mass increases. How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Be prepared to show your reasoning.</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> Elena needs to compare the slope of the data for hybrids to the slope of the data for new cars. She could do this by looking at the scatter plots and graphing an approximated line of best for each scatter plot. She could then see which line of best fit looks like it is decreasing faster or find and compare the slopes of each approximated line of best fit.</p>
</div>
</div>
<!--End interaction-->
<br>