Average rate of change
Initial explanation
The average rate of change is given by the rate of change of both variables.
"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:
Δy/Δx
("Δ" means "change").
We want to analyze the change over the interval 3 ≤ x ≤ 9.
Step 1: change of x (Δx)
The change from x = 3 and x = 9 is
Δx = 9 - 3 = 6
Step 2: change of y (Δy)
We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.
The change from y = 28 to y = 4 is
Δy = 4 - 28 = -24
Step 3: rate of change
Then, the average rate of change is:
Δy/Δx = -24/6 = -4
Answer: -4