1. GRADIENTS AND STRAIGHT LINE GRAPHS

2. The gradient of a straight line is a measure of how steep the line is.
horizontal distance
vertical distance
gradient =
vertical distance
horizontal distance
These lines have positive gradient.
These lines have negative gradient.

3. 1 Find the gradient of the line.5 4
Gradient = 5 4

4. 2 Find the gradient of the line.3 6 1 2
Gradient = = 3 6

5. 3 Find the gradient of the line.5
Gradient =
= 1 5 5

6. 4 Find the gradient of the line.
− 6 2
Gradient =
= − 3 6 2

7. 5 Find the gradient of the line.
− 4 6
− 2 3
Gradient = = 4 6

8. 6 Find the gradient of the line joining the points (−2, 1) and (4, 5).y
4 6 2 3
Gradient = = 4 6 x

9. 7 Find the gradient of the line joining the points (−1, 3) and (2, −3).y
− 6 3
Gradient =
= −2 x 6 3

10. The gradient of a line passing through two points can also be calculated using a formula.
If the points are (x1, y1) and (x2, y2) then the gradient (m) is given by
Examples
1 Find the gradient of the line joining the points (2, 1) and (8, 7).
Gradient =

11. 2 Find the gradient of the line joining the points (−2, 1) and (4, 5).

12. Straight line graphs of the form y = ax + b
1 Draw the graph of y = 2x + 1. y x -2 -4 2 4
Choose 3 values of x and work out the corresponding y values. x
y = 2x + 1
When x = 0, y = 2 × = 1 x
When x = 1, y = 2 × = 3 x
When x = 2, y = 2 × = 5
Put the results into a table. x 1 2 y 3 5
Plot the points on a graph and join with a straight line.

13. 2 Draw the graph of y x When x = 3, y = 2 - ⅓ × 3 = 1 x-2 -4 2 4
When x = 3, y = 2 - ⅓ × 3 = 1 x
When x = 0, y = 2 - ⅓ × 0 = 2 x x
When x = −3, y = 2 - ⅓ × -3 = 3 x −3 3 y 2 1

14. Straight line graphs of the form ax + by = c
1 Draw the graph of 3x + 4y = 12. y x -2 -4 2 4
The easiest method is to find the axis crossing points. x
When x = 0, 4y = 12 so y = 3.
3x + 4y = 12
When y = 0, 3x = 12 so x = 4. x
Put the results into a table. x 4 y 3
Plot the points on a graph and join with a straight line.

15. The easiest method is to find the axis crossing points.
2 Draw the graph of 2x - 3y = 6. y x -2 -4 2 4
The easiest method is to find the axis crossing points.
When x = 0, −3y = 6 so y = −2.
When y = 0, 2x = 6 so x = 3. x
Put the results into a table. x x 3 y −2
2x - 3y = 6
Plot the points on a graph and join with a straight line.