©G Dear2008 – Not to be sold/Free to use Stage 4 Year 9 Coordinate Geometry Download Geogebra Gradient Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use

Gradient of a Line Gradient is the rate of change. Vertical Rise Horizontal Run 1 2 3 4 5 6 7 (5,7) rise run m m = 4 7-3 5-1 4 4 (1,3) = = 1 GeoGebra

Gradient of a Line 6 m = -4 rise m = run 3 = -2 -3 = 2 (1,7) 6 7-1 5 6 7 (1,7) m = 6 -4 m = rise run = 3 -2 6 7-1 (5,1) = -3 2 1-5 -4

Gradient of a Line Gradients can be: Positive An Increasing function Zero Horizontal Negative A Decreasing function

Gradient of a Line rise m = run y2-y1 = x2-x1 y (x2,y2) y2-y1 x2-x1 3 4 5 6 7 (x2,y2) rise run m = y2-y1 y2-y1 = x2-x1 x2-x1 (x1,y1) y

Gradient of a Line Gradient of (4,2) to (8,10)? y2-y1 10-2 8 4 m = = = (x1,y1) (x2,y2) Gradient of (4,2) to (8,10)? y2-y1 10-2 8 4 m = = = = 2 x2-x1 8-4 (x1,y1) (x2,y2) Gradient of (5,9) to (7,3)? y2-y1 3-9 -6 2 m = = = = -3 x2-x1 7-5