Linear or exponential: x 0, 1, 2, 3; y 10, 8, 6, 4

Step by step

The question

Question: is this table linear or exponential: x is 0, 1, 2, 3, and y is 10, 8, 6, 4?

We write it as a table.

x goes up by 1 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: minus 2, then minus 2, then minus 2.

We add -2 every time.

The same number.

So the table is linear.

2 Write the rule

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 −2x.

At x = 0, y is 10, not 0.

The start value goes in too.

So the rule is y = −2x + 10.

3 Check

Let's check with the last pair: x = 3.

The rule gives 4.

The table says 4.

So the rule is right!

Let's look back.

First: check the differences.

Then: write the rule.

Last: check.