Step by step
The question
Question: write the equation for this table: x is 1, 2, 3, 4, and y is 7, 9, 11, 13.
x: 1, 2, 3, 4; y: 7, 9, 11, 13
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 2 when x goes up by 1.
Change in y on top.
Change in x at the bottom.
= m = 21
m = change in y ÷ change in x
2 Start value
The start value is y when x is 0.
The table starts at x = 1.
We go back one step to x = 0: take away 2.
y at 0 is 5.
= b = 7 − 2 = 5
Careful!
7 is y at x = 1.
The start value is y at x = 0.
Careful: not b = 7 ✗
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 = 2x + 5.
= y = 2x + 5
4 Check
Let's check with the last pair: x = 4.
The equation gives 13.
The table says 13.
So the answer is right!
x = 4: 2 × 4 + 5 = 13
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 2x + 5