Write the equation: x 2, 4, 6, 8; y 1, 4, 7, 10

Step by step

The question

Question: write the equation for this table: x is 2, 4, 6, 8, and y is 1, 4, 7, 10.

We write it as a table.

1 Rate of change

Rate of change means: how much y changes when x goes up by 1.

y changes by 3 when x goes up by 2.

Change in y on top.

Change in x at the bottom.

That is 1.5 for each 1 of x.

Careful!

x goes up by 2, not 1.

So we divide the change of y by 2.

2 Start value

The start value is y when x is 0.

The table starts at x = 2.

We go back 2 steps to x = 0: take away 1.5 each time.

y at 0 is −2.

3 Write the equation

A line is y = m x plus b: m is the rate of change, b is the start value.

So the equation is y = 1.5x − 2.

4 Check

Let's check with the last pair: x = 8.

The equation gives 10.

The table says 10.

So the answer is right!

Let's look back.

First: rate of change.

Then: start value.

Then: write the equation.

Last: check.