Step by step
The question
Question: write the equation for this table: x is 1, 3, 5, 7, and y is 10, 4, −2, −8.
x: 1, 3, 5, 7; y: 10, 4, −2, −8
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 −6 when x goes up by 2.
Change in y on top.
Change in x at the bottom.
That is −3 for each 1 of x.
= m = −62 = −3
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 = −6 ✗
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: add 3.
y at 0 is 13.
= b = 10 + 3 = 13
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 + 13.
= y = −3x + 13
4 Check
Let's check with the last pair: x = 7.
The equation gives −8.
The table says −8.
So the answer is right!
x = 7: −3 × 7 + 13 = −8
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = −3x + 13