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<h3 class="wp-block-heading">Key Concepts</h3>



<p>1. Linear Association</p>



<p>2. Strength of Linear Association</p>



<p>3. Recognise Non Linear Association</p>



<ol class="wp-block-list">
<li>Recognise different patterns of scatter plots&nbsp;</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="225" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548-1024x225.png" alt="" class="wp-image-14933" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548-1024x225.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548-300x66.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548-768x169.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548-1536x338.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-548.png 1600w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<ol class="wp-block-list" start="2">
<li>Recognise different types of correlation&nbsp;</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="330" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-550-1024x330.png" alt="" class="wp-image-14936" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-550-1024x330.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-550-300x97.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-550-768x247.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-550.png 1406w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<ol class="wp-block-list" start="3">
<li>Recall what is a slope of a line&nbsp;&nbsp;</li>
</ol>



<p>Slope of a line measures the steepness and direction of line.&nbsp;&nbsp;</p>



<p>slope = rise/ run&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



<p>Rise is the vertical change between two points, where as run is the horizontal change&nbsp; between two points.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="294" height="288" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-549.png" alt="" class="wp-image-14934"/></figure></div>


<ol class="wp-block-list" start="4">
<li>Recall different methods to find the slope of a line , slope-intercept formula, two point formula&nbsp;&nbsp;</li>
</ol>



<ul class="wp-block-list">
<li>Slope is constant through out the line .&nbsp;</li>
</ul>



<ul class="wp-block-list">
<li>The slope – intercept formula for a line is y= mx + b, where m is the slope of the line and b is the y-intercept of the line.&nbsp;</li>



<li>If (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>) are any two points on a line then slope of a line&nbsp;</li>
</ul>



<p>is (y<sub>2</sub> – y<sub>1</sub>)/(x<sub>2</sub> – x<sub>1</sub>).&nbsp;</p>



<p>m = (y<sub>2</sub> – y<sub>1</sub>)/(x<sub>2</sub> – x<sub>1</sub>)&nbsp;</p>



<p>slope of a horizontal line is zero and slope of a vertical line is not defined.&nbsp;</p>



<ol class="wp-block-list">
<li>If the rise is 20 units and run is 10 units then the slope of the line is&#8212;&#8212;&#8211;&nbsp;</li>
</ol>



<ol class="wp-block-list" start="2">
<li>Y= 2x + 1 is an equation of a straight line then the slope of the line is&#8212;&#8212;&#8212;&nbsp;</li>
</ol>



<h3 class="wp-block-heading">Line of best fit&nbsp;</h3>



<p><a href="https://www.turito.com/learn/math/line-of-best-fit-grade-10">Line of best fit</a> is a line through a scatter plot of data points that best expresses the relationship between those points. </p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="307" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-552-1024x307.png" alt="" class="wp-image-14937" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-552-1024x307.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-552-300x90.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-552-768x230.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-552.png 1537w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<h2 class="wp-block-heading"><strong>Linear Association</strong>&nbsp;</h2>



<p>When a straight line describes the relation between two variables then it is a <a href="https://www.turito.com/learn/math/linear-associations-grade-8" data-type="link" data-id="https://www.turito.com/learn/math/linear-associations-grade-8">linear Association</a>.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="983" height="440" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-547.png" alt="" class="wp-image-14932" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-547.png 983w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-547-300x134.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-547-768x344.png 768w" sizes="auto, (max-width: 983px) 100vw, 983px" /></figure></div>


<p><strong>Example 1:</strong>&nbsp;</p>



<p>Georgia and her classmates are measuring their height and arm span. They record their data in a table.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="379" height="327" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-551.png" alt="" class="wp-image-14935" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-551.png 379w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-551-300x259.png 300w" sizes="auto, (max-width: 379px) 100vw, 379px" /></figure></div>

<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="201" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-553-1024x201.png" alt="" class="wp-image-14938" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-553-1024x201.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-553-300x59.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-553-768x151.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-553.png 1166w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<p>How can they determine what relationship, if any, exists between the two sets of <a href="https://www.turito.com/learn/physics/measurement-of-distances" data-type="link" data-id="https://www.turito.com/learn/physics/measurement-of-distances">measurements</a>?&nbsp;</p>



<p><strong>Step 1: </strong>Plot the data points in a scatter plot.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="351" height="354" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-554.png" alt="" class="wp-image-14939" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-554.png 351w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-554-297x300.png 297w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-554-150x150.png 150w" sizes="auto, (max-width: 351px) 100vw, 351px" /></figure></div>

<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="351" height="386" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-561.png" alt="" class="wp-image-14946" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-561.png 351w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-561-273x300.png 273w" sizes="auto, (max-width: 351px) 100vw, 351px" /></figure></div>


<p class="has-text-align-left"><strong>Step 2: </strong>Use a pencil to find a line that passes through the middle of the plotted points. This line is called a <strong>trend line</strong>.&nbsp;</p>



<p><strong>Step 3:</strong> Look at the slope of the line. The slope is positive.&nbsp;</p>



<p>Georgia can draw a trend line on the scatter plot to determine that there is a positive relationship between height and arm span.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="351" height="361" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-555.png" alt="" class="wp-image-14940" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-555.png 351w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-555-292x300.png 292w" sizes="auto, (max-width: 351px) 100vw, 351px" /></figure></div>


<h3 class="wp-block-heading">Perfect Linear Association&nbsp;</h3>



<p>Relationship between two variables is a perfect linear relationship, then a scatterplot of the points will fall on a straight line.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="423" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-556-1024x423.png" alt="" class="wp-image-14941" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-556-1024x423.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-556-300x124.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-556-768x317.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-556.png 1065w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<h3 class="wp-block-heading">Strong Linear Association&nbsp;</h3>



<p>The more the points tend to fall along a straight line the stronger the linear relationship. &nbsp;</p>



<p>When the slope is 1 there occurs a strong linear association.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="805" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-557-1024x805.png" alt="" class="wp-image-14942" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-557-1024x805.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-557-300x236.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-557-768x604.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-557.png 1343w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<h3 class="wp-block-heading">Weak&nbsp;Linear Association&nbsp;</h3>



<p>A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="822" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-558-1024x822.png" alt="" class="wp-image-14943" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-558-1024x822.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-558-300x241.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-558-768x617.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-558.png 1344w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<h3 class="wp-block-heading">Non Linear Association&nbsp;</h3>



<p>A nonlinear relationship is a type of relationship between two entities in which change in one entity does not correspond with constant change in the other entity.&nbsp;&nbsp;</p>



<p>An association between two variables in which the direction and rate of change fluctuate.&nbsp;&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="558" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559-1024x558.png" alt="" class="wp-image-14944" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559-1024x558.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559-300x164.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559-768x419.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559-1536x837.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-559.png 1600w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<h2 class="wp-block-heading"><strong>Analysing Linear Association</strong>&nbsp;</h2>



<p>The easy way to interpret a linear association is using slope-intercept formula <strong>y=m x + c </strong>, where&nbsp;<strong> </strong>&nbsp;<br><strong>m</strong> is the slope of the line and <strong>c</strong> is the y intercept.&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-large"><img loading="lazy" decoding="async" width="1024" height="317" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560-1024x317.png" alt="" class="wp-image-14945" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560-1024x317.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560-300x93.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560-768x237.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560-1536x475.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-560.png 1562w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure></div>


<p>Scatter plots can show a linear association, a nonlinear association, or no association. For scatter plots that suggest&nbsp; a linear association, you can draw a trend line to show the association. You can assess the strength of the association by looking at the distances of plotted points from the trend line.</p>



<h2 class="wp-block-heading">Exercise:</h2>



<p>1. What is line of best?</p>



<p>2. What is linear association?</p>



<p>3. How do you analyse a linear association?</p>



<p>4. What is Perfect linear association?</p>



<p>5. What is the slope of strong linear association?</p>



<p>6. Draw a graph giving non linear association?</p>



<p>7. What is the slope of horizonatal line?</p>



<p>8. What is the slope of vertical line?</p>



<p>&nbsp;</p>
