Graphs - Lesson 2 by apteacher

mathematics · @apteacher · Apr 1 '18

$5.40

Graphs - Lesson 2

<html>
<h1>Linear and non-linear graphs</h1>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100424.png" width="454" height="452"/></p>
<p><a href="http://www.mathfunny.com/images/algebra-graphing-trigonometry-line-graph-linear-equation.jpg">Source</a></p>
<p>After the lesson of yesterday, we now know the difference between the <a href="https://steemit.com/mathematics/@apteacher/graphs-lesson-1">dependent</a> and <a href="https://steemit.com/mathematics/@apteacher/graphs-lesson-1">independent</a> variable.</p>
<p><br></p>
<p>The relationship between two variables can also be linear, non-linear or constant</p>
<h2>We can analyze graphs using the following:</h2>
<h3>Linear:</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100403.png" width="638" height="335"/></p>
<p><a href="http://s3-ap-southeast-1.amazonaws.com/subscriber.images/maths/2016/07/13114551/Graphs-300x163.png">Source</a></p>
<p>When the relationship between the dependent and independent variable is linear, the graph will look like the example above, a straight line.</p>
<h3>Non-linear graph</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100404.png" width="695" height="314"/></p>
<p><a href="https://gpsgate.com/images/uploads/Capture2.PNG">Source</a></p>
<p>When the relationship between the dependent and independent variable is non-linear, the line is not a straight line.</p>
<h3>Constant:</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100407.png" width="292" height="187"/></p>
<p><a href="https://byjus.com/physics/wp-content/uploads/2016/01/0-45-300x197.png">Source</a></p>
<p>When the relationship between the dependent and independent variable is constant, the line will be parallel to the x-axis. &nbsp;The dependent variable will stay the same as the independent variable will change.</p>
<p><br></p>
<h3>Increasing, decreasing and constant graphs</h3>
<p>As we are busy with line graphs, we can also say if the are increasing, decreasing or staying constant.</p>
<p>Look at the different examples given:</p>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100409.png" width="258" height="271"/></p>
<p><a href="https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/1227/2015/04/03010639/CNX_Precalc_Figure_02_01_004abc2.jpg">Increasing graph</a></p>
<p>An increasing graph is from small to big, going upwards mean that the graph is increasing</p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100410.png" width="270" height="271"/></p>
<p><a href="https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/1227/2015/04/03010639/CNX_Precalc_Figure_02_01_004abc2.jpg">Decreasing graph</a></p>
<p>A decreasing graph is going in a downwards direction. &nbsp;From big to small.</p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100411.png" width="248" height="274"/></p>
<p><a href="https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/1227/2015/04/03010639/CNX_Precalc_Figure_02_01_004abc2.jpg">Constant graph</a></p>
<p>A constant graph doesn't increase or decrease but stays the same.</p>
<p>We can ask learners to do the following:</p>
<p>Represent the following relationships on a line graph. &nbsp;Place the dependent variable on the y-axis and the independent variable on the x-axis.</p>
<h3>1. &nbsp;There is a linear relationship between the windspeed and temperature. &nbsp;As the windspeed increases, the temperature drops at a constant rate.</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100413.png" width="476" height="268"/></p>
<p>The learners graph will look something like the example above, remember that no further information was given, only that the windspeed increases and the temperature drops. &nbsp;Learners have to know that the temperature is dependent on the windspeed. &nbsp;If the wind does not blow, the temperature won't drop.</p>
<p><br></p>
<h3>2. &nbsp;The relationship between the butterfly population is non-linear and increasing</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100414.png" width="475" height="269"/></p>
<p>The butterfly population is dependent on time. &nbsp;If time does not go by, we won't be able to see if the population is increasing or decreasing. &nbsp;The question only asks that learners must draw a line graph, where the population of the butterflies are increasing in a non-linear relationship. &nbsp;This means that the graph can't be a straight line.</p>
<p><br></p>
<h3>3. &nbsp;The pressure in a space craft is kept constant.</h3>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100415.png" width="471" height="270"/></p>
<p>The pressure in a space craft is kept constant, this means, as the space craft needs speed to go into space, as the speed increases, the pressure will stay the same.</p>
<p><br></p>
<p>For the examples above, learners can use their own information of how fast the speed will be etc. The idea of this activity is just to see that learners know which relationship will be on the x or y-axis, and if they know what increasing, decreasing and constant graphs will look like.</p>
<p><img src="https://imgoat.com/uploads/8b3eff8baf/100416.gif" width="589" height="100"/>&nbsp;</p>
</html>

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