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Gradient of a straight line x y 88 66 44 22 02468 44 4 For the graph of y = 2x 4 rise run = 8 4 = 2 8 rise = 8 4 run = 4 Gradient = y = 2x 4

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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

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Gradient of a straight line x y 88 66 44 22 02468 44 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)

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Gradient of a straight line x y 88 66 44 22 02468 44 4 To calculate the gradient of the line y = 2x + 4, choose any two points on the line. 4 4 0 = 8 4 = 22 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

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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

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Lesson 2: The Equation of a Line The Equation of a Line is: y = mx + b Where m is the slope And b is the y-intercept.

Lesson 2: The Equation of a Line The Equation of a Line is: y = mx + b Where m is the slope And b is the y-intercept.

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