You can identify **parallel lines **by recognising the fact that they have **the same gradient**.

**e.g. y = 3x + 1 and y = 3x - 7 are parallel, as they both have a gradient of 3.**

**e.g. y = 3x + 1 and y = 7 - 3x are not parallel. The first line has a gradient of 3, whereas the second has a gradient of - 3.**

We need to make sure that the equations of any line are in the form **y = mx + c, **as this is the only way of finding what the gradient is.

If the equation of the line has a different form, we need to rearrange it to the form **y = mx + c**, where **m** represents the gradient of the line.

Let's put this knowledge into practise now.

**e.g. Two lines have the equations y = 5x + 2 and 2y + 6 = 10x. Are these two lines parallel?**

y = 5x + 2 is already in the correct form, so it can stay as it is.

The gradient of this line is **5**.

2y + 6 = 10x is not in the correct form, so we need to rearrange it.

2y = 10x - 6

y = 5x - 3

The gradient of the second line is **5**.

As the gradients of both lines are **5**, they **are** parallel.

In this activity, we will identify if lines are parallel by comparing gradients represented by m in the equation y = mx + c.