It is possible to work out the gradient of a straight line from the coordinates of any two points which lie on the line, either by drawing the line or simply by subtracting and dividing coordinates.
Gradient of line = | y-step |
x-step |
Remember that the line will have positive or negative gradient.
Example
Find the gradient of the straight line which passes through (8, 5) and (5, 9)
Answer 1
Let's look at the line drawn on a set of x-y coordinate axes.
The vertical part of the step (y-step) = -4
The horizontal part of the step (x-step) = 3
Gradient of line = | y-step | = | -4 | |
x-step | 3 |
Answer 2
It is possible to work out the gradient WITHOUT drawing the line.
Look at the coordinates of the two points (8, 5) and (5, 9).
We can get the y-step by subtracting the y-coordinates.
y-step = 5 - 9 = -4
In the same order, we get the x-step by subtracting the x-coordinates:
x-step = 8 - 5 = 3
Gradient of line = | y-step | = | -4 | |
x-step | 3 |
NB We could have worked out 9 - 5 = 4 and 5 - 8 = -3 but 4 ÷ -3 = -4 ÷ 3