In this activity, we will build on what we know about parallel and perpendicular lines.

We know that a straight line graph is in the form:

**y = mx + c**

where m is the gradient and C is the y-intercept.

**Parallel lines**

**Parallel lines have the same gradient.**

All of these lines have a gradient of 5.

** Perpendicular Lines**

**Perpendicular lines have gradients which multiply together to give -1.**

Here, one line has a gradient of 5 and the other of -1/5.

To find the gradient of a line which is perpendicular to one of gradient a/b, we invert the fraction and multiply by -1.

This is called the **'negative reciprocal'.**

Don't worry - it's easier than it sounds!

We are going to use all this information to find straight lines which are parallel and perpendicular!

Let's look at a typical question!

__Example__

State the straight line which is parallel to

**y = 2x + 5**

and goes through the point (0, 3)

**Answer**

From the straight line

**y = 2x + 5**

We can see that the** gradient m is 2**

For a line to be parallel, it must have the **same gradient.**

y = 2x + C will be parallel.

Our line also passes through (0, 3) which is the y-intercept C

Therefore, the answer is:

**y = 2x + 3**

We do exactly the same for a perpendicular line, but instead of the gradient m repeated we find the negative reciprocal.

That is the inverse and x by -1

So, if the gradient was 2, then the perpendicular gradient is -1/2

Let's try some questions!