Linear or exponential: x 0, 2, 4, 6; y 1, 7, 13, 19

Step by step

The question

Question: is this table linear or exponential: x is 0, 2, 4, 6, and y is 1, 7, 13, 19?

We write it as a table.

x goes up by 2 each time.

1 Check the differences

Linear means: the same number is added each time.

So we look at the change from one y to the next: plus 6, then plus 6, then plus 6.

We add 6 every time.

The same number.

So the table is linear.

2 Write the rule

y changes 6 when x goes up 2.

For each 1 of x, that is 3.

A linear rule is y = m x plus b.

m is the change when x goes up 1.

b is the start value, at x = 0.

Careful!

Not just 3x.

At x = 0, y is 1, not 0.

The start value goes in too.

So the rule is y = 3x + 1.

3 Check

Let's check with the last pair: x = 6.

The rule gives 19.

The table says 19.

So the rule is right!

Let's look back.

First: check the differences.

Then: write the rule.

Last: check.