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8. 4. For the graph of y = 2 x 4. y. 4. rise = 8. x. 8. 6. 4. 2. 0. 2. 4. 6. 8. run = 4. 4. y = 2 x 4. rise. 8. 2. Gradient =. . =. . =. run. 4. y 2 y 1. x 2 x 1. For the graph of y = mx + c. y. ( x 2 , y 2 ) . rise = y 2 y 1.
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8 4 For the graph ofy = 2x 4 y 4 rise = 8 x 8 6 4 2 0 2 4 6 8 run = 4 4 y = 2x 4 rise 8 2 Gradient = = = run 4
y2 y1 x2 x1 For the graph ofy = mx+ c y (x2, y2) rise = y2 y1 0 x (x1, y1) run = x2 x1 y = mx+ c y2 y1 rise Gradient = = x2 x1 run
4 (4) 4 0 To calculate the gradient of the liney = 2x 4, choose any two points on the line. y (4, 4) 4 e.g., (x1, y1) = (0, 4) x and (x2, y2) = (4, 4) 8 6 4 2 0 2 4 6 8 y2 y1 Gradient = x2 x1 (0, 4) 4 4 (4) = 4 0 y = 2x 4 8 2 = = 4
8 4 To calculate the gradient of the liney = 2x+ 4, choose any two points on the line. y y = 2x+ 4 (0, 4) 4 e.g., (x1, y1) = (0, 4) x and (x2, y2) = (4, 4) 8 6 4 2 0 2 4 6 8 y2 y1 Gradient = x2 x1 (4, 4) 4 4 4 = 4 0 8 2 = = 4
y y (x2, y2) (x2, y2) x x 0 0 (x1, y1) (x1, y1) Positive gradient: Negative gradient: y values increase y values decrease asx values increase asx values increase