SAT Math Multiple Choice Question 542: Answer and Explanation
The scatterplot above shows data collected from 10 major league baseball players comparing the average weekly time each one spent in batting practice and the number of home runs he hit in a single season. The line of best fit for the data is also shown. What does the slope of the line represent in this context?
- A. The estimated time spent in batting practice by a player who hits 0 home runs
- B. The estimated number of single-season home runs hit by a player who spends 0 hours in batting practice
- C. The estimated increase in time that a player spends in batting practice for each home run that he hits in a single season
- D. The estimated increase in the number of single-season home runs hit by a player for each hour he spends in batting practice
Correct Answer: D
Category: Problem Solving and Data Analysis / Scatterplots
Strategic Advice: You don't need to know the slope of the line of best fit to answer the question, so don't waste valuable time trying to find it. Instead, use the labels on the axes to determine the meaning of the slope.
Getting to the Answer: Graphically, slope is the ratio of the change in the y-values (rise) to the change in the x-values (run). In a real-world scenario, this is the same as the unit rate. In this context, the rise describes the change in the number of home runs hit in a single season, and the run describes the change in the number of hours a player spends in batting practice. Thus, the unit rate, or slope, represents the estimated increase (since the data trends upward) in the number of single-season home runs hit by a player for each hour he spends in batting practice.