Step by step
The question
Question: write the equation for this table: x is 3, 4, 5, 6, and y is −1, 1, 3, 5.
x: 3, 4, 5, 6; y: −1, 1, 3, 5
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 = 3.
We go back 3 steps to x = 0: take away 2 each time.
y at 0 is −7.
= b = −1 − 3 × 2 = −7
Careful!
−1 is y at x = 3.
The start value is y at x = 0.
Careful: not b = −1 ✗
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 − 7.
= y = 2x − 7
4 Check
Let's check with the last pair: x = 6.
The equation gives 5.
The table says 5.
So the answer is right!
x = 6: 2 × 6 − 7 = 5
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 2x − 7