Step by step
The question
Question: write the equation for this table: x is 2, 3, 4, 5, and y is 9, 12, 15, 18.
x: 2, 3, 4, 5; y: 9, 12, 15, 18
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 1.
Change in y on top.
Change in x at the bottom.
= m = 31
m = change in y ÷ change in x
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 3 each time.
y at 0 is 3.
= b = 9 − 2 × 3 = 3
Careful!
9 is y at x = 2.
The start value is y at x = 0.
Careful: not b = 9 ✗
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 = 3x + 3.
= y = 3x + 3
4 Check
Let's check with the last pair: x = 5.
The equation gives 18.
The table says 18.
So the answer is right!
x = 5: 3 × 5 + 3 = 18
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 3x + 3