1. ©G Dear2008 – Not to be sold/Free to use
Stage 4
Year 9
Coordinate
Geometry
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Geogebra
Gradient
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©G Dear2008 – Not to be sold/Free to use

2. 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
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3. Gradient of a Line 6 m = -4 rise m = run 3 = -2 -3 = 2 (1,7) 6 7-15 6 7
(1,7)
m = 6 -4
m =
rise
run = 3 -2 6
7-1
(5,1) = -3 2
1-5 -4

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

5. Gradient of a Line rise m = run y2-y1 = x2-x1 y (x2,y2) y2-y1 x2-x13 4 5 6 7
(x2,y2)
rise
run
m =
y2-y1
y2-y1 =
x2-x1
x2-x1
(x1,y1) y

6. 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