The table shows a linear relationship between x and y. x: 0, 1, 2… Step by Step

Step by step

The question

Question: write the equation for this table: x is 0, 1, 2, 3, and y is 40, 35, 30, 25.

x: 0, 1, 2, 3; y: 40, 35, 30, 25

We write it as a table.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Rate of change

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

y changes by −5 when x goes up by 1.

Change in y on top.

Change in x at the bottom.

m = −51

That is the rule for m.

m = change in ychange in x

2 Start value

The start value is y when x is 0.

The table has x = 0: y is 40.

b = 40

3 Write the equation

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

y = mx + b

So the equation is y = −5x + 40.

y = −5x + 40

4 Check

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

The equation gives 25.

The table says 25.

So the answer is right!

x = 3: −5 × 3 + 40 = 25

5 Pick the choice

Our answer is y = −5x + 40.

That is choice B.

B) y = −5x + 40

6 Why not the others

A is y = −5x + 25.

Wrong: 25 is the last y: the start is y at x = 0.

A) y = −5x + 25 ✗ 25 is the last y: the start is y at x = 0

C is y = 5x + 40.

Wrong: y goes down: the rate is −5.

C) y = 5x + 40 ✗ y goes down: the rate is −5

D is y = 40x − 5.

Wrong: the start and the rate swapped.

D) y = 40x − 5 ✗ the start and the rate swapped

Let's look back.

First: rate of change.

Then: start value.

Then: write the equation.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer