In this activity, we will be looking at how sequences link to straight line graphs.

Let's take the sequence:

### 2, 4, 6, 8 ,10, .........

We can see that this is the 2 times table, so the rule for this is **2n**

What about

### 3, 5, 7, 9, 11, ........

This still goes up in 2's so the rule is 2n, but each term is **not **2, 4, 6 etc

Each term is 1 more than the 2 times table.

Therefore, our rule for this one is **2n + 1**

We can apply this rule to recognising and drawing straight line graphs.

We use y and x, but it is just a sequence of coordinates which join to form a straight line.

**See the graph of y = 2x + 1 below:**

As in the sequence, the line starts at y = 1 and goes up in 2's (that is 1 across, 2 up)

We can recognise a straight line graph because it** goes up or down by a constant value** (2 in this case).

If the x was x^{2} or x^{3} etc it would not be constant, so would form a curve.

Let's look at a typical question!

__Example__

Which of the equations below form a straight line graph?

**y = 3x - 5 y = 2x + x ^{2}**

**Answer**

**y = 3x - 5** is the answer as it goes up by 3, which is **constant.**

The x^{2} term in the other equation makes the graph form a curve.

Let's have a go at some questions!