1. “Teach A Level Maths” Vol. 1: AS Core Modules
1: Straight Lines and Gradients

2. Finding the Gradient 4 2

5. is The gradient of the straight line joining the points and
To use this formula, we don’t need a diagram!
e.g. Find the gradient of the straight line joining the points and
Solution:

6. The gradient of the straight line joining the points
and is

7. Find the gradient of the line joining the points A(3,–2) and B(–5,6)
x1= 3 y1= –2
x2 = –5 y2 = 6

8. Find the gradient of the line joining the points A(3,–2) and B(–5,6)
x1 = 3 y1= –2
x2 = –5 y2 = 6

9. m is the gradient of the line
The equation of a straight line is
m is the gradient of the line
c is the point where the line meets the y-axis,
the y-intercept
e.g has gradient m =
and y-intercept, c =
gradient = 2 x
intercept on y-axis

10. e.g. Substituting x = 4 in gives
gradient = 2 x
intercept on y-axis
( 4, 7 ) x
The coordinates of any point lying on the line satisfy the equation of the line
e.g. Substituting x = 4 in gives
showing that the point ( 4,7 ) lies on the line.

11. Finding the equation of a straight line when we know
its gradient, m and
the coordinates of a point on the line (x1,y1).
Using , m is given, so we can find c by
substituting for y, m and x.
e.g. Find the equation of the line with gradient
passing through the point
Solution:
(-1, 3) x
Add 2 to both sides
C = 5
So,

12. Using the formula when we are given two points on the line
e.g. Find the equation of the line through the points
Solution: First find the gradient
Now use with
We could use the 2nd point,
(-1, 3) instead of (2, -3)
Add 4 to both sides
-3 = -4 + c

13. SUMMARY
Equation of a straight line
where m is the gradient and c is the intercept on the y-axis
Gradient of a straight line
where and are points on the line

14. Exercise
1. Find the equation of the line with gradient 2 which passes through the point
Solution:
So,
2. Find the equation of the line through the points
Solution:
So,

15. We sometimes rearrange the equation of a straight line so that zero is on the right-hand side ( r.h.s. )
e.g can be written as
We must take care with the equation in this form.
e.g. Find the gradient of the line with equation
Solution: Rearranging to the form :
so the gradient is