Step by step
The question
Question: write the equation for this table: x is 0, 2, 4, 6, and y is 10, 7, 4, 1.
x: 0, 2, 4, 6; y: 10, 7, 4, 1
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.
= m = −32 = −1.5
m = change in y ÷ change in x
Careful!
x goes up by 2, not 1.
So we divide the change of y by 2.
Careful: not m = −3 ✗
2 Start value
The start value is y when x is 0.
The table has x = 0: y is 10.
= b = 10
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 = −1.5x + 10.
= y = −1.5x + 10
4 Check
Let's check with the last pair: x = 6.
The equation gives 1.
The table says 1.
So the answer is right!
x = 6: −1.5 × 6 + 10 = 1
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = −1.5x + 10