Determine average rate of change from a graph representing data. | Two-variable data: Models and scatterplots | SAT Math

Core Idea

Average rate of change between two points is the slope of the line connecting them: $Δ 𝑦 Δ 𝑥$ . It tells you how fast one quantity changes per unit of the other, on average, over that interval.

Understanding

Average rate of change is the slope between two points on the graph.

Find the change in $𝑦$ .
Find the change in $𝑥$ .
Divide $Δ 𝑦$ by $Δ 𝑥$ .
Interpret the unit in context.

If the graph is linear, the average rate of change is constant. If it curves, the interval matters.

Step by Step

Identify the two points: (x1, y1) and (x2, y2).
Compute the change in y: y2 − y1.
Compute the change in x: x2 − x1.
Divide: $𝑦 2 - 𝑦 1 𝑥 2 - 𝑥 1$ . Include units in your answer.

Misconceptions

Confusing average rate of change with the instantaneous rate at one point. Average rate of change uses two points and covers an interval.
Reversing the subtraction order. If you flip the order in the numerator, you must also flip it in the denominator — or the sign will be wrong.
Thinking the average rate of change tells you what happened at each individual moment.

Question

Worked Example

The graph below shows the total number of books sold by a bookstore over a 10-week period. At week 2, the store had sold 120 books. At week 8, the store had sold 450 books. What is the average rate of change, in books per week, of books sold from week 2 to week 8?

Select an answer to see the explanation