year 8 maths

7D
Gradient
415
7D Gradient
EXTENSION
The gradient of a line is a measure of how steep the line is. The
steepness or slope of a line depends on how far it rises or falls over
a given horizontal distance. This is why the gradient is calculated
by dividing the vertical rise by the horizontal run between two
points. Lines that rise (from left to right) have a positive gradient
and lines that fall (from left to right) have a negative gradient.
Positive gradient
Negative gradient
Let’s start: Which is the steepest?
At a children’s indoor climbing centre there are three types of sloping walls to climb.
The blue wall rises 2 metres for each metre across. The red wall rises 3 metres for
every 2 metres across, and the yellow wall rises 7 metres for every 3 metres across.
• Draw a diagram showing the slope of each wall.
• Label your diagrams with the information given above.
• Discuss which wall might be the steepest, giving reasons.
• Discuss how it might be possible to accurately compare the slope of each wall.
Wall
■ The gradient is a measure of slope .
• It is the increase in y as x increases by 1 .
• It is the ratio of the change in y over the change in x .
rise
• Gradient =
run
• Rise = change in y
• Run = change in x
• The run is always considered to be positive when
moving from left to right on the Cartesian plane.
• The two diagrams show a positive rise and a
negative rise .
■ A gradient is negative if y decreases as x increases.
The rise is considered to be negative.
3
1
Positive gradient
2
2
4
Negative gradient
Gradient = rise
run
= 4 2
= 2 1
= 2
Gradient = rise
run
= −3
2
Key ideas
■ The gradient of a horizontal line is zero .
2
= − 3 2
■ The gradient of a vertical line is undefined, which means
there is no numerical value assigned to this gradient .
Gradient =
0
2
= 0
Gradient =
2 , which is undefined.
0
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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