1. The gradient of a line
The gradient of a line is a specific term for the steepness of a straight line.
We all have an in-built sense of steepness and can order the steepness of lines.
However, the gradient gives a numerical value to this general understanding.

2. To calculate the gradient of a line we count the vertical distance that line increases and horizontal distance that the line and then use the following calculation.
vertical change
gradient =
horizontal change

3. 4 6 A B 6 3 C D 7 1 E F
Gradient AB =
vertical
horizontal = 6 4 =
1.5

4. A B C

5. Note: A negative gradient means that the line is travelling downhill or a decline.

6. Calculating the gradient from co-ordinates
It is possible to calculate the gradient of a line just by knowing two co-ordinates that the line passes through.
This can be achieved in two ways:
1. Draw the co-ordinates on a grid and use the previous method.
Change in x
horizontal =

7. 2. Using a formula that has been specifically
2. Using a formula that has been specifically generated for the calculation.
Let a line pass through two co-ordinates (X1,Y1) and (X2,Y2).
Change in x
X2 - X1 =

8. (X2,Y2)
Y2 - Y1
(X1,Y1)
X2 - X1

9. Calculate the gradient of the line between the following
pairs of co-ordinates.
1. (1,2) and (5,18)
X2 - X1 = m
5 - 1 = 4 = = 4
Note: The gradient of a line is more usually given the label (m).

10. 2. (7,5) and (3,13)
X2 - X1 = m
3 - 7 = -4 = = -2
3. (4, -2) and (-2, -5)
X2 - X1 = m =
- 6 = =

11. 3. (4, -2) and (-2, -5) x y x
(4, -2) 3 x 6
(-2, -5)