Gradient of a straight line x y 88 66 44 2 44 4 For the graph of y = 2x  4 rise run  = 8  4 = 2 8 rise = 8 4 run = 4 Gradient = y = 2x  4

Gradient of a straight line x y 0 For the graph of y = mx + c rise run  = y2  y1y2  y1  x2  x1x2  x1 y2  y1y2  y1 rise = y 2  y 1 x2  x1x2  x1 run = x 2  x 1 Gradient = (x 1, y 1 )  (x 2, y 2 )  y = mx + c

Gradient of a straight line x y 88 66 44 2 44 4 To calculate the gradient of the line y = 2x  4, choose any two points on the line. 4  (  4) 4  0  = 8  4 = 2 Gradient = y = 2x  4 e.g., (x 1, y 1 ) = (0,  4)  x2  x1x2  x1 y2  y1y2  y1 = 4  (  4) 4  0 and (x 2, y 2 ) = (4, 4) (4, 4)  (0,  4) 

Gradient of a straight line x y 88 66 44 2 44 4 To calculate the gradient of the line y =  2x + 4, choose any two points on the line.  4 4  0  = 8  4 = 22 Gradient = y =  2x + 4 e.g., (x 1, y 1 ) = (0, 4)  x2  x1x2  x1 y2  y1y2  y1 = 4 and (x 2, y 2 ) = (4,  4)  (4,  4)  (0, 4) 8 

Gradient of a straight line x y 0 (x 2, y 2 ) (x 1, y 1 ) y values increase x y (x 2, y 2 ) (x 1, y 1 ) 0 Positive gradient: as x values increase y values decrease Negative gradient: as x values increase