# Lesson video

In progress...

Hi, I'm Miss Davies.

In this lesson, we're going to be working out the gradient of a line perpendicular to a given line.

What is meant by perpendicular? Lines that's a perpendicular meet at 90 degrees.

The gradient of this line is one.

This is its perpendicular line.

The gradient of this line is negative one.

The gradient of this next line is two.

The gradient of its perpendicular line is negative a half.

The next line has a gradient of negative two-thirds.

The gradient of its perpendicular line is three over two.

The gradient of this line is a half.

The gradient of its perpendicular is negative two.

What do you notice about the gradients? The gradients of the two perpendicular lines multiply to make negative one.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

The gradients of the perpendicular lines should multiply to get negative one.

In this example, we've been asked to find the gradient of a line that is perpendicular to Y equals two X add one.

The gradient of the line Y equals two X add one is two.

We know that when you multiply the gradients of two perpendicular lines, you get negative one.

Negative one divided by two will give us the gradient of the perpendicular line.

One divided by negative two is negative one-half.

Therefore, the gradient of a line perpendicular is negative one-half.

In this next example, we've been asked to find the gradient of a line perpendicular to Y add two-thirds X is equal to one.

To find the gradient of this line, we need to make Y the subject.

We're going to do this by subtracting two-thirds X from each side.

This gives us Y is equal to one subtract two-thirds X.

This means that the gradient of the line is negative two-thirds.

To calculate the gradient of the line perpendicular, we are going to divide negative one by negative two-thirds.

This gives us three over two.

Therefore, the gradient of the line perpendicular is three over two.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.