Basics of straight lines

There are several basic facts and equations connected with straight lines that you need to know by heart.

Distance formula

The distance between two points, and is given by the formula:

So the distance between and is:

The gradient m between two points and is given by the formula:

This only applies where . If then the gradient is undefined.

• If a line with gradient makes an angle with the positive direction of the -axis then

Example 1

We can calculate the gradient of the line above by selecting two coordinate points that the straight line passes through.

(1,2) and (2,5)

Now that we know the gradient, we can calculate the angle that the straight line makes with the positive direction of the axis.

Similarly, we can calculate the gradient of the straight line if we know the angle the line makes with the positive direction of the axis.

Example 2

This time you will notice, the line has a negative gradient, so you will need to use your knowledge of quartiles to calculate this gradient.