{"id":156206,"date":"2022-03-26T01:29:56","date_gmt":"2022-03-25T19:59:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/linear-graph\/"},"modified":"2025-06-24T14:25:18","modified_gmt":"2025-06-24T08:55:18","slug":"linear-graph","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/","title":{"rendered":"Linear Graph"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Explain_in_Detail_Linear_Graph_Equation\" title=\"Explain in Detail :Linear Graph Equation\">Explain in Detail :Linear Graph Equation<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Line_Graph_Definition\" title=\"Line Graph Definition\">Line Graph Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Line_Graph_Meaning\" title=\"Line Graph Meaning\">Line Graph Meaning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Linear_Graph_Equation\" title=\"Linear Graph Equation\">Linear Graph Equation<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#General_Form\" title=\"General Form\">General Form<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Slope_Intercept_Form\" title=\"Slope Intercept Form\">Slope Intercept Form<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Linear_Diagram\" title=\"Linear Diagram\">Linear Diagram<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#How_to_graph_a_linear_equation\" title=\"How to graph a linear equation?\">How to graph a linear equation?<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Plot_Points\" title=\"Plot Points\">Plot Points<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#X_and_Y-Intercepts\" title=\"X and Y-Intercepts\">X and Y-Intercepts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Slope-Intercept\" title=\"Slope-Intercept\">Slope-Intercept<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-graph\/#Solved_Examples\" title=\"Solved Examples\">Solved Examples<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_Linear_Graph_Equation\"><\/span>Explain in Detail :Linear Graph Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear graph equation is an equation in which the independent variable is linear. This means that the equation can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156205 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-graph.jpg\" alt=\"Linear Graph\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-graph.jpg?v=1648238395 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-graph-300x212.jpg?v=1648238395 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h3 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"Line_Graph_Definition\"><\/span><b>Line Graph Definition<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">What is linear? Linear means a straight line. And what is a graph? A graph is a pictorial representation of our data in an organized manner. So we can say that a graph when plotted gives a single straight line then it is said to be a linear graph.<\/span><\/p>\n<p style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Linear relationships are used in our day to day life. These relationships can be expressed in many different ways. Linear graphs, when graphed they give a straight line. Linear graphs can be sketched or plotted on graph paper.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Line_Graph_Meaning\"><\/span><b>Line Graph Meaning<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">When a set of data varies with time, we usually use a line graph to represent them. In a line graph, the data are usually plotted against time and each pair of adjacent data points is joined by a straight line segment. The main advantage of using a line graph to represent data is that we can observe the trend of the movement of data. Hence, we may use a line graph to forecast certain future data values.<\/span><\/p>\n<p style=\"font-weight: 400;\">Now it is clear that what is linear, we can define it as,<\/p>\n<p style=\"font-weight: 400;\">Sometimes, the graph is a single straight line. Such a graph is called a linear graph.<\/p>\n<p style=\"font-weight: 400;\">To draw a linear graph, we need to locate some points on the graph paper. Join these points. If the line joining these points is a straight line, then it is a linear graph.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Linear_Graph_Equation\"><\/span><b>Linear Graph Equation<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">A linear equation or an equation of a straight line.<\/p>\n<h4 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"General_Form\"><\/span><b>General Form<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"font-weight: 400;\">\n<li>ax + by + c = 0, where a, b, c are constants.<\/li>\n<\/ul>\n<h4 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"Slope_Intercept_Form\"><\/span><b>Slope Intercept Form<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"font-weight: 400;\">\n<li>y = mx + b, where m is the gradient or the slope and b is the y-intercept.<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\"><b>Point Slope Form<\/b><\/p>\n<ul style=\"font-weight: 400;\">\n<li>y &#8211; y1 = m (x &#8211; x1), where m is the gradient or slope and x1 and y1 are coordinates of a given point.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Linear_Diagram\"><\/span><b>Linear Diagram<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"font-weight: 400;\">A linear diagram can represented as follows:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_to_graph_a_linear_equation\"><\/span><b>How to graph a linear equation?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">We can plot a graph by three methods they are:<\/p>\n<h4 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"Plot_Points\"><\/span><b>Plot Points<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol style=\"font-weight: 400;\">\n<li>Take any value for x.<\/li>\n<li>Substitute the value of x in the equation to find the value of y.<\/li>\n<li>Plot the x and y values on the graph.<\/li>\n<li>To plot another point repeat step 1.<\/li>\n<li>Join the two points and we get the straight line.<\/li>\n<\/ol>\n<h4 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"X_and_Y-Intercepts\"><\/span><b>X and Y-Intercepts<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol style=\"font-weight: 400;\">\n<li>Set y=0 to find the x-intercept and solve for x.<\/li>\n<li>Set x=0 to find the y-intercept and solve for y.<\/li>\n<li>Now plot the x-intercept and the y-intercept on the graph.<\/li>\n<li>Join the two points and we get a straight line.<\/li>\n<\/ol>\n<h4 style=\"font-weight: 400;\"><span class=\"ez-toc-section\" id=\"Slope-Intercept\"><\/span><b>Slope-Intercept<\/b><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol style=\"font-weight: 400;\">\n<li>Plot the point after you find the y-intercept.<\/li>\n<li>Use the slope and find the another point and plot it using the y-intercept.<\/li>\n<li>Join the two points and we get a straight line.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Solved_Examples\"><\/span><b>Solved Examples<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\"><b>Example 1<\/b>: Observe the graph given and write it in slope-intercept form i.e y = mx + b.<\/p>\n<p style=\"font-weight: 400;\"><b>Solution:<\/b><\/p>\n<p style=\"font-weight: 400;\">Given<\/p>\n<p style=\"font-weight: 400;\">The slope is 1<\/p>\n<p style=\"font-weight: 400;\">The y intercept is -1<\/p>\n<p style=\"font-weight: 400;\">Substitute this into y=mx+b<\/p>\n<p style=\"font-weight: 400;\">we get  y = x &#8211; 1<\/p>\n<p style=\"font-weight: 400;\">So the equation is y = x -1<\/p>\n<p style=\"font-weight: 400;\"><b>Example 2: Find the equation of the straight line that has slope m = 2 and passes through the point (\u20131, \u20134).<\/b><\/p>\n<p style=\"font-weight: 400;\"><b>Solution<\/b>: By the slope-intercept form we have;<\/p>\n<p style=\"font-weight: 400;\">y=mx+c<\/p>\n<p style=\"font-weight: 400;\">Given,<\/p>\n<p style=\"font-weight: 400;\">m=2<\/p>\n<p style=\"font-weight: 400;\">we have;<\/p>\n<p style=\"font-weight: 400;\">y = -4 and x = -1<\/p>\n<p style=\"font-weight: 400;\">Substitute the values in the above equation, we get<\/p>\n<p style=\"font-weight: 400;\">-4 = 2(-1) + c<\/p>\n<p style=\"font-weight: 400;\">-4 = -2 + c<\/p>\n<p style=\"font-weight: 400;\">c = -4 &#8211; 2 = -6<\/p>\n<p style=\"font-weight: 400;\">Hence, the required equation will be;<\/p>\n<p style=\"font-weight: 400;\">y = 2x &#8211; 6<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Explain in Detail :Linear Graph Equation A linear graph equation is an equation in which the independent variable is linear. 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