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onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1061/functions.html">Functions</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">2.5 Linear models</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <h2><img alt="" src="../../files/MM/LM/LMsmall-1.jpg" style="width: 100px; height: 100px; float: left;">Straight line functions</h2> <p>Commonly seen in the form y = f(x) = mx + c where m represents the gradient/rate of change of the function and c is the y-intercept, where x = 0. These models are a fundamental bit of algebra that come up again and again. they are also fairly commonly used models. For example an electricity bill often has a standing charge that you pay even before you have used any electricity (this is the y - intercept, because amount of electricity used, x = 0) and then a given amount for every unit of electricity used (this is the gradient of the cost graph - it goes up by this amount for every unit of electricity used)</p> <hr> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-c3fd70db-7fff-27f4-41d9-81952a0a1358"></span></p> <p dir="ltr"><span id="docs-internal-guid-c3fd70db-7fff-27f4-41d9-81952a0a1358">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Understand the general expression of a linear function <span class="math-tex">\(y=mx+c\)</span> with gradient and y-intercept</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Understand that linear functions model situations where there is a constant rate of change</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Derive and use linear models</p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides Gallery</p> </div> </div> <div class="panel-body"> <div> <p>Use these slides to review the material and key points covered in the videos.</p> <div id="carousel-242" class="dynamic-gallery carousel slide" data-id="242"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-242/linear-no-logos001.jpeg" data-fancybox="gallery-242" title="" data-caption=""><img alt="" src="../../../std-galleries/15-242/linear-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-242/linear-no-logos002.jpeg" data-fancybox="gallery-242" title="" data-caption=""><img alt="" src="../../../std-galleries/15-242/linear-no-logos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-242/linear-no-logos003.jpeg" data-fancybox="gallery-242" title="" data-caption=""><img alt="" src="../../../std-galleries/15-242/linear-no-logos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-242/linear-no-logos004.jpeg" data-fancybox="gallery-242" title="" data-caption=""><img alt="" src="../../../std-galleries/15-242/linear-no-logos004.jpeg"></a></div><div class="item "><a class="fancy" 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fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-242" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos005-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos006-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos007-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-242/linear-no-logos008-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Linear Functions</p> </div> </div> <div class="panel-body"> <div> <p>This video is about the nature of linear relationships and how they appear as plotted functions on a coordinates grid.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591595523"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Plotting linear functions</p> </div> </div> <div class="panel-body"> <div> <p>This video goes through the process of plotting linear functions from the equations.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591595910"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Fractional Gradients</p> </div> </div> <div class="panel-body"> <div> <p>This video covers linear functions with fractional gradients</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591596220"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Negative gradients</p> </div> </div> <div class="panel-body"> <div> <p>This video covers linear functions with negative gradients</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591596505"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Examples</p> </div> </div> <div class="panel-body"> <div> <p>This video looks at lots of examples of linear functions</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591597107"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Other Forms</p> </div> </div> <div class="panel-body"> <div> <p>What happens when the function/relation is not shown as y = mx + c?</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591597402"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Finding values</p> </div> </div> <div class="panel-body"> <div> <p>This video looks at a linear function in context finding the value of one of the variables when you know the other.</p> </div> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591597686"></iframe></div> </div> </div> </div> </div> </div> <h4> </h4> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p>This section of the page can be used for quick review. The flashcards help you go over key points and the quiz lets you practice answering questions on this subtopic.</p> <p>Review these condensed 'key point' flashcards to help you check and keep ideas fresh in your mind.</p> <div id="carousel-243" class="dynamic-gallery carousel slide" data-id="243"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-243/linear-no-logos001.jpeg" data-fancybox="gallery-243" title="" data-caption=""><img alt="" src="../../../std-galleries/15-243/linear-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-243/linear-no-logos002.jpeg" data-fancybox="gallery-243" title="" data-caption=""><img alt="" src="../../../std-galleries/15-243/linear-no-logos002.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-243" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-243" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-243/linear-no-logos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-243/linear-no-logos002-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.</p> <h4> </h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-316-2207"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>A linear function has a y - intercept of 3 and a gradient of 2.5, which of the following is it?</p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> <img align="middle" alt="f left parenthesis x right parenthesis equals 3 over 2 x plus 5 over 2" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«mi»x«/mi»«mo»+«/mo»«mfrac»«mn»5«/mn»«mn»2«/mn»«/mfrac»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-23.php?formula=50b40f83da4c5d0c5189c544a88512d7.png"></label></p><p><label class="checkbox"><input type="checkbox"> <img align="middle" alt="f left parenthesis x right parenthesis equals 3 x plus 2.5" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo».«/mo»«mn»5«/mn»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-24.php?formula=62d42732204aa9a95b44d0d242bff9f0.png"></label></p><p><label class="checkbox"><input class="c" type="checkbox"> <img align="middle" alt="f left parenthesis x right parenthesis equals 5 over 2 x plus 3" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»5«/mn»«mn»2«/mn»«/mfrac»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-22.php?formula=701afb6e9b8b66f20db4546a033dce39.png"></label></p></div><div class="q-explanation"><p><img align="middle" alt="5 over 2" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»5«/mn»«mn»2«/mn»«/mfrac»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-26.php?formula=f3efef5f99ecb0b6a36ec7add667024d.png"> is 2.5 and this is the number multiplied by x, the gradient</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear function 3x + 2y = 18, what is the the y - intercept?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="9"> <span class="review"></span> </p></div><div class="q-explanation"><p>At the y - intercept, x = 0, so 2y = 18 and y = 9</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear function 5x - 2y - 8 = 0. It crosses the y - axis at the point (0,-4), what is its gradient?</p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> -2.5</label></p><p><label class="checkbox"><input type="checkbox"> -5</label></p><p><label class="checkbox"><input class="c" type="checkbox"> 2.5</label></p><p><label class="checkbox"><input type="checkbox"> 5</label></p></div><div class="q-explanation"><p>Rearrange to get 2y = 5x - 8 and then divide by 2 to get y = 2.5x - 4</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following is the correct equation for the graph in the picture?</p><p style="text-align: center;"><img alt="" src="../../files/MM/LM/Q3.jpg" style="width: 400px; height: 280px;"></p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> y = 0.25x + 4</label></p><p><label class="checkbox"><input class="c" type="checkbox"> y = 0.25x - 1</label></p><p><label class="checkbox"><input type="checkbox"> y = 4x + 0.25</label></p><p><label class="checkbox"><input type="checkbox"> y = 4x - 1</label></p></div><div class="q-explanation"><p>Gradient is positive and 0.25, y intercept is - 1 </p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following graphs is the function y = -3x + 2?</p><p style="text-align: center;"><img alt="" src="../../files/MM/LM/Q4.jpg" style="width: 400px; height: 344px;"></p></div><div class="q-answer"><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input class="c" type="checkbox"> C</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input type="checkbox"> A</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input type="checkbox"> B</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input type="checkbox"> D</label></p></div><div class="q-explanation"><p>Gradient is negative 3 and intercept is positive 2.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Check the functions you can see on the diagram below?</p><p style="text-align: center;"><img alt="" src="../../files/MM/LM/Q6.jpg" style="width: 500px; height: 410px;"></p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> y = -4x + 1</label></p><p><label class="checkbox"><input class="c" type="checkbox"> y = x - 2</label></p><p><label class="checkbox"><input class="c" type="checkbox"> y = -2x - 1</label></p><p><label class="checkbox"><input type="checkbox"> y = 4x</label></p><p><label class="checkbox"><input type="checkbox"> y = 2x + 2</label></p><p><label class="checkbox"><input class="c" type="checkbox"> y = -3x + 2</label></p></div><div class="q-explanation"><p>Remember that gradient is 'Rise/Run' </p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear model, f(x) = 3.42x -1.7, what is the value of the function when x = 4? Give your answer to 3sf.</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="12.0"> <span class="review"></span> </p></div><div class="q-explanation"><p><img align="middle" alt="f left parenthesis x right parenthesis space equals space 3.42 space cross times 4 space minus 1.7f left parenthesis x right parenthesis space equals space 11.98f left parenthesis x right parenthesis space equals space 12.0 space left parenthesis 3 s f right parenthesis" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mo».«/mo»«mn»42«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mn»1«/mn»«mo».«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»11«/mn»«mo».«/mo»«mn»98«/mn»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»12«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»(«/mo»«mn»3«/mn»«mi»s«/mi»«mi»f«/mi»«mo»)«/mo»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-27.php?formula=3f05bd713cfcd146dab4f057dc433fdf.png"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear model, f(x) = -0.04x + 100, what is the value of the function when x = 5.5? Give your answer to 3sf.</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="99.8"> <span class="review"></span> </p></div><div class="q-explanation"><p><img align="middle" alt="f left parenthesis x right parenthesis space equals space minus 0.04 cross times 5.5 space plus space 100f left parenthesis x right parenthesis space equals space 111.76f left parenthesis x right parenthesis space equals space 112 space left parenthesis 3 s f right parenthesis" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«mn»04«/mn»«mo»§#215;«/mo»«mn»5«/mn»«mo».«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»111«/mn»«mo».«/mo»«mn»76«/mn»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»112«/mn»«mo»§#160;«/mo»«mo»(«/mo»«mn»3«/mn»«mi»s«/mi»«mi»f«/mi»«mo»)«/mo»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-28.php?formula=542a981428490a898f9a5aacb8f1197e.png"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear model, f(x) = -0.04x + 100, what is the value of x when the f(x) = 99? </p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="25"> <span class="review"></span> </p></div><div class="q-explanation"><p><img align="middle" alt="99 equals negative 0.04 x space plus space 100minus 1 space equals negative space 0.04 xx space equals space 25" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»99«/mn»«mo»=«/mo»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«mn»04«/mn»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»100«/mn»«mspace linebreak=¨newline¨/»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»04«/mn»«mi»x«/mi»«mspace linebreak=¨newline¨/»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»25«/mn»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-30.php?formula=3a2903cebe724e12f7a8011d24c92b0e.png"> or input y = - 0.004x + 100 in your GDC and read from the table.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider the linear model, f(x) = 3.42x -1.7, what is the value of x when f(x) = 49.6?</p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="15"> <span class="review"></span> </p></div><div class="q-explanation"><p><img align="middle" alt="49.6 space equals space 3.42 x space minus space 1.751.3 space equals space 3.42 xx space equals space 15" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»49«/mn»«mo».«/mo»«mn»6«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mo».«/mo»«mn»42«/mn»«mi»x«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo».«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mn»51«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mo».«/mo»«mn»42«/mn»«mi»x«/mi»«mspace linebreak=¨newline¨/»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»15«/mn»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-25.php?formula=6e577f3f4d66ba1831756ff97a1e3c71.png"> or input y = 342x - 1.7 in to your GDC and read from the table.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/MM/LM/LMQ1.jpg" style="width: 700px; height: 767px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/591599512"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" 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