2The Straight Line Equation Learning IntentionTo explain and draw straight lines of the form y = mx + c.
3The Straight Line Equation By calculating the gradient of each line, write down the equation of the lineyThe Straight Line Equation12435x
4The Straight Line Equation Gradient = vertical heighthorizontal distance= 41= 4Equation of line is y = 4xLine 2Gradient = vertical heighthorizontal distance= 32Equation of line is y = 3x2Line 3Gradient = vertical heighthorizontal distance= 22= 1Equation of line is y = x
5The Straight Line Equation Gradient = vertical heighthorizontal distance= 12Equation of line is y = 1x2Gradient = vertical heighthorizontal distance= 14Line 5Equation of line is y = 1x4
6The Straight Line Equation All the lines we have previously looked atall passed through the origin at (0,0)i.e. y = 2x, y = 3x, y = ½x, y = 5x etc…Gradient = 3Gradient = 5Gradient = 2Gradient = ½What about straight lines that do not pass through the origin
7The Straight Line Equation ExampleDraw the line of y = 2x on a suitable coordinate diagramy = 2x + 2yxSame gradient, but slightly higher upy2468y = 2xOn the same diagram, draw the graph of y = 2x + 2xy2(0)+22(0)+22(0)+22(3)+22(4)+2=2=4=6=8=10xWhat do you notice about the second line?
8The Straight Line Equation ExampleDraw the line of y = x on a suitable coordinate diagramyxy = x + 4Same gradient, but slightly higher upy1234y = xOn the same diagram, draw the graph of y = x + 4xy45678xWhat do you notice about the second line?
9The Straight Line Equation y = xOn your 4 quadrant diagram, Draw the lines of the given equations.The Straight Line Equation12345678910-9-8-7-6-5-4-3-2-1-10xyxy24y = 3x+124xy12147y = x - 3y = 2x + 3xy48xy12-315357
10Straight Line Equation y10lines are parallel if they have the same gradientAll straight lines havethe equation of the form98y = mx + c76543Where linemeets y-axis2Gradient1x12345678910Find the equations of the following linesy = xy = x+4y = 4x+2y = -0.5x+2
11Straight Line Equation Now try Ex 4Ch6 Page 73Start at Q4