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<h4>Activity</h4>
<p>What if the point you are given isn’t a \( y \)-intercept? Point-slope is a great form to use when you are given the slope and any point. </p>
<p>First, work to derive the point-slope formula by completing the following steps:</p>
<p>Start with the slope formula as \( m= \frac{y-y_1}{x-x_1} \).</p>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="47449637-a56f-4f2f-9f60-77c89eb8c0a9" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Step 1 - Multiply both sides of the equation by \( x - x_1 \).</p>
</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: \( m(x-x_1)=\left(\frac{y-y_1}{x-x_1}\right)(x-x_1) \)</p>
</div>
</div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="40d72c4f-b9cd-4524-9c7d-9be5dace35f8" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Step 2 - Simplify.</p>
</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: \( m(x-x_1)=y-y_1 \)</p>
</div>
</div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d22f1f8e-c204-4d56-a9e4-50d7de126c98" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Step 3 - Rewrite the equation with the \(y\) terms on the left.</p>
</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: \( y - y_1 = m(x - x_1) \)</p>
</div>
</div>
<br>
<!--Q1-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="eventShow1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<p>With your partner, you will find the equation of the line in point-slope form that goes through the point \( (3, 4) \) and has a slope of 2 by answering the following questions.</p>
<br>
<br>
<ol class="os-raise-noindent">
<li>Use the point and slope to graph the line on a coordinate plane.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, and then 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="eventShow1">
<p>Compare your answer:</p>
<img alt class="img-fluid atto_image_button_text-bottom" height="313" role="presentation" src="https://k12.openstax.org/contents/raise/resources/390f352c17676b18164cb6fe769e1ef7b67d2889" width="400"> <br>
<br>
</div>
<br>
<!--Q2-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="eventShow1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="2">
<li>Write the point-slope form.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, and then 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="eventShow1">
<p>Compare your answer: </p>
<p>\( y-y_1=m(x-x_1) \)</p>
</div>
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3addce7a-5294-4111-ab82-ba83b95d7fbc" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Name the point \( (x_1, y_1) \) and the slope, \( m \).</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><span>\( x_1=3,\ y_1=4,\ m =2 \)</span><br>
</p>
</div>
</div>
<br>
<!--Q4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1a5f9bf0-bc15-4f8f-b2dd-fd11545b4b2c" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>Substitute the point and slope into the point-slope form.</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>\( y -4 =2(x-3) \)</p>
</div>
</div>
<br>
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="24534d77-e4cd-4710-9723-978072f99fc2" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>Now, with your partner, each solve for \(y\) to write the equation in slope-intercept form. Compare your answers for any possible errors. Come to an agreement on your equation. You may also choose to graph the line on a coordinate plane using a graphing calculator or Desmos with your final equation to check your answer.</li>
</ol>
<p>What is the simplified equation in slope-intercept form \((y = mx + b)\)?</p>
</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>\( y = 2x - 2 \)</p>
</div>
</div>
<br>
<br>
<!--Q#6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="59aacdb6-71fd-498f-a5ce-c8d858561360" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>Convert slope-intercept form to standard form. </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>\(2x -y=2\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-student-reflection">
<p class="os-raise-student-reflection-title">Building Character: Social Intelligence</p>
<div class="os-raise-d-flex-nowrap os-raise-gap-1">
<img height="200" src="https://k12.openstax.org/contents/raise/resources/28cebef2dd7dc23448276a6d2a6943cc8d852cb6" width="200px">
<div>
<p class="os-raise-mb-0">Being empathetic, or sensitive to what others are feeling, shows that you care about others. In fact, empathetic people are less likely to experience anxiety, depression, and addictions later in life. They are also more likely to be hired, promoted, earn more money, and have happier marriages and better-adjusted children.</p>
<p>Think about your current sense of social intelligence. Are the following statements are true for you?</p>
<ul>
<li>
My relationships make me feel good about myself.
</li>
<li>
The people in my life help me be my best.
</li>
</ul>
<p>Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!</p>
</div>
</img>
</div>
</div>