How do you find the equation of a line through two points?

First find the gradient

If the two points have coordinates (x1,y1) and (x2, y2) then the gradient (m) is given by:

x1 - x2

y1 - y2

The equation of the line is y = mx + c

To find c, plug in the coordinates of one of the points and rearrange the equation to get c =

You can then put this value of c into the equation for the straight line

Let's say point 1 has co-ordinates (a, b) and point 2 has co-ordinates (c, d).

Find the change in the y co-ordinates: d - b

Find the change in the x co-ordinates: c - a

The gradient, m, of the line will be (d - b) divided by (c - a). Let's call it e.

Write the equation of a straight line replacing m with e: y = ex + c

Now use either point 1 or point 2 (it doesn't matter which you use) and substitute the x and y values into the equation.

Choosing point 1: b = e(a) + c

Now solve this equation to find the value of c, let's call it f.

The equation of the line will be y = ex + f.

Example: Point 1 (2, 5) Point 2 (6, 9)

Change in y = 9 - 5 = 4

Change in x = 6 - 2 = 4

m = 4 divided by 4 = 1

y = x + c

Use point 1: 5 = 2 + c

c = 3

y = x + 3