A straight line graph is a sequence of numbers which go up or down by the gradient.

**For example**

**3, 5, 7, 9, ......** has the rule ** 2n + 1** because it goes up in 2s and each term is 1 more than the 2 times table.

When we draw a straight line graph with a gradient of 2 and a y-intercept of 1 we write **y = 2x + 1.**

If we plot the table of values we find that sequence:

Therefore, we can create our own coordinates if we have the straight line graph.

Where are we going with this? Let's look at a question to make it clearer.

__Example__

Does the point (15, 49) lie on the line y = 3x + 4?

__Answer__

Firstly, we look at y = 3x + 4 and we know that:

**the gradient is 3** (it goes up in 3s)

**the y-intercept is +4 ** (so, we know that (0, 4) is a point on the line)

If we take the point **(15, 49)** it means that **when x = 15 then y = 49**

If it lies on the line y = 3x + 4 **we should be able to substitute these values in** and the equation should be true!

If the equation is** not **equal then the point does not lie on the line!

Let's try some of these questions.