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Understanding Line Gradient Calculation: Clear Steps and Examples

Learn how to calculate the gradient of a line with step-by-step instructions and examples using the formula y = mx + c. Understand positive and negative gradients and how y values change with x values.

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Understanding Line Gradient Calculation: Clear Steps and Examples

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  1. 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

  2. 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

  3. 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

  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

  5. 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

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