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href="../186/mathematics.html">Mathematics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Linear graphs</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../maths/math-9.jpg" style="float: left; width: 250px; height: 167px;">A linear graph refers to any straight line relationship. </p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <h4>Equation</h4> <p>A straight line can be described by the following equation:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(y = mx+c\)</span></p> <ul> <li><span class="math-tex">\(m\)</span> is the gradient</li> <li><span class="math-tex">\(c\)</span> is the y-intercept</li> </ul> </div> <h4>Practical skills </h4> <ul> <li>If there are error bars drawn on a graph from an experiment, then it must be possible to place your ruler inside all of the error bars at once for the graph to be <em>linear.</em></li> <li>A <em>proportional</em> graph refers to the special case where the line is straight and passes through the origin (0,0). Experiments can be used to verify proportional relationships such as Ohm's Law and Hooke's Law.</li> </ul> <h4>Tutorial</h4> <p>This video shows the effects of changing <span class="math-tex">\(m\)</span> and <span class="math-tex">\(c\)</span> on the appearance of the line.</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/159605824"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-purple"> <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><em>Predict the effect of moving the sliders.</em></p> <p style="text-align: center"><iframe height="351px" scrolling="no" src="https://www.geogebra.org/material/iframe/id/WQE8gUff/width/453/height/351/border/888888/rc/false/ai/false/sdz/false/smb/false/stb/false/stbh/true/ld/false/sri/false/at/auto" style="border:0px;" width="453px"></iframe></p> </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> <p><i>Use quizzes to practise application of theory.</i></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#51d707ed"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="51d707ed"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Linear <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-31-189" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>What is the gradient of the following graph</p><p style="text-align: center;"><img alt="" src="../../images/linearq1.png" style="width: 340px; height: 231px;"></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1/3</label></p><p><label class="radio"><input type="radio"> 3</label></p><p><label class="radio"><input class="c" type="radio"> 2</label></p><p><label class="radio"><input type="radio"> 1/2</label></p></div><div class="q-explanation"><p>change in y/change in x = 2/1</p></div><div class="slide-q-actions"><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="exercise shadow-bottom"><div class="q-question"><p>What is the equation of the following line</p><p style="text-align: center;"><img alt="" src="../../images/linearq1.png" style="width: 340px; height: 231px;"></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> y = 3x + 1</label></p><p><label class="radio"><input type="radio"> y = 3x - 0.5</label></p><p><label class="radio"><input class="c" type="radio"> y = 2x +1</label></p><p><label class="radio"><input type="radio"> y = 2x - 0.5</label></p></div><div class="q-explanation"><p>Y = (gradient) + (y intercept)</p></div><div class="slide-q-actions"><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="exercise shadow-bottom"><div class="q-question"><p>The gradient of the line in the following graph is:</p><p style="text-align: center;"><img alt="" src="../../images/linearq2.png" style="width: 308px; height: 229px;"></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 3</label></p><p><label class="radio"><input type="radio"> 1</label></p><p><label class="radio"><input class="c" type="radio"> -1</label></p><p><label class="radio"><input type="radio"> -3</label></p></div><div class="q-explanation"><p>change in y is negative so gradient = -3/3</p></div><div class="slide-q-actions"><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="exercise shadow-bottom"><div class="q-question"><p>The following line can be represented by the equation y = mx + c</p><p style="text-align: center;"><img alt="" src="../../images/linearq2.png" style="width: 308px; height: 229px;"></p><p>What is the value of c?</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 3</label></p><p><label class="radio"><input type="radio"> -1</label></p><p><label class="radio"><input type="radio"> -3</label></p><p><label class="radio"><input type="radio"> 1</label></p></div><div class="q-explanation"><p>c is the y intercept</p></div><div class="slide-q-actions"><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> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> 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