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

核心知识

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.

深入理解

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.

分步讲解

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.

常见误解

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.

题目

示例解析

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?

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