05 February 2022 Equations of lines Gradient intercept

05 February 2022 Equations of lines: Gradient- intercept form LO: To draw a graph from the equation in the form gradient-intercept form. www. mathssupport. org

Equation of a line, gradient-intercept form The gradient-intercept form of the equation of the straight line with gradient m and y-intercept c is y = mx + c Example 1. State the gradient and y-intercept of the line with equation y = 3 x + 2 and c = 2 m=3 the gradient is 3 and y-intercept is 2 Example 2. State the gradient and y-intercept of the line with equation y = 7 – 2 x m = – 2 and c = 7 the gradient is – 2 and y-intercept is 7 www. mathssupport. org

Graphing from the gradient-intercept form Drawing the graph of a line in gradient-intercept form To draw the graph of a line in the form y = mx + c q Use the y-intercept c to plot the point (0, c) q Starting from the point (0, c), use horizontal and vertical steps from the gradient m to locate another point on the line. q Join the two points and extend the line in either direction. www. mathssupport. org

Graphing from the gradient-intercept form y Graph the line with equation y = 2 x + 3 10 9 8 7 3 is the y intercept. run = 16 5 We need one other point on the graph. The other point can be found by using the gradient. 2 is the gradient. It means: rise = 2 run = 1 rise = 2 4 3 X y intercept = 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 www. mathssupport. org y = 2 x + 3 X 1 2 3 4 5 6 7 8 9 10 x

Graphing from the gradient-intercept form y Graph the line with equation y = 2 x - 3 10 9 8 7 -3 is the y intercept. 6 5 We need one other point on the graph. The other point can be found by using the gradient. 2 is the gradient. It means: rise = 2 run = 1 4 3 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 rise = 2 0 -1 -2 1 X 2 3 4 5 run = 1 6 7 8 9 10 X -3 -4 -5 -6 -7 -8 -9 -10 www. mathssupport. org y = 2 x - 3 2 y intercept = -3 x

Graphing from the gradient-intercept form y Graph the line with equation y = x - 4 10 9 8 7 -4 is the y intercept. 6 We need one other point on the graph. The other point can be found by using the gradient. 1 is the gradient. It means: rise = 1 run = 1 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 run -2= 1 rise = 1 -3 X -4 X -5 -6 -7 -8 -9 -10 www. mathssupport. org y=x-4 5 y intercept = -4 x

Graphing from the gradient-intercept form y Graph the line with equation y = 3 x - 4 10 9 8 7 -4 is the y intercept. 6 We need one other point on the graph. The other point can be found by using the gradient. 3 is the gradient. It means: rise = 3 run = 1 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 rise = 3 -2 1 X 2 3 4 5 6 7 8 9 10 run = 1 -3 -4 X -5 -6 -7 -8 -9 -10 www. mathssupport. org y = 3 x - 4 5 y intercept = -4 x

Graphing from the gradient-intercept form y Graph the line with equation y = 43 x + 2 10 9 8 7 2 is the y intercept. run = 4 We need one other point on the graph. The other point can be found by using the gradient. 3 4 is the gradient. It means: rise = 3 run = 4 rise = 3 6 4 3 2 X y intercept = 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 www. mathssupport. org X 5 1 2 3 4 5 6 7 8 9 10 x

Graphing from the gradient-intercept form y Graph the line with equation y = -2 x + 1 10 9 8 1 is the y intercept. 7 We need one other point on the graph. 5 The other point can be found by using the gradient. -2 is the gradient. It means: rise = -2 run = 1 6 y intercept = 1 4 3 2 rise = -2 1 X -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 run =-2 1 -3 -4 -5 -6 -7 -8 -9 -10 www. mathssupport. org y = -2 x + 1 1 X 2 3 4 5 6 7 8 9 10 x

Graphing from the gradient-intercept form y Graph the line with equation y = - 54 x + 3 10 9 8 3 is the y intercept. 7 We need one other point on the graph. 5 The other point can be found by using the gradient. - 54 is the gradient. It means: rise = -4 run = 5 4 3 X rise = -4 1 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 run = 5 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 www. mathssupport. org y intercept = 3 6 1 2 3 4 5 X 6 7 8 9 10 x

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