SAT Math Multiple Choice Question 425: Answer and Explanation

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Question: 425

5.

Increased physical activity has been linked to a lower incidence rate of diabetes. The scatterplot above shows the relationship between the percent of people in a certain country whose daily activity qualifies them as "inactive" and the incidence rate of diabetes in that country. The line of best fit for the data is also shown. Which of the following best represents the meaning of the y-intercept of the line of best fit in the context of this question?

  • A. The predicted incidence rate of diabetes when the entire country is considered active
  • B. The predicted incidence rate of diabetes when the entire country is considered inactive
  • C. The predicted percent of people who will be active when the incidence rate of diabetes is 0%
  • D. The predicted percent of people who will be inactive when the incidence rate of diabetes is 0%

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: You don't need to know the y-intercept 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 y-intercept.

Getting to the Answer: The y-intercept is the point at which x = 0. In this real-world scenario, the percent of people who are considered inactive is graphed on the x-axis, so the y-intercept occurs when 0% of the country is inactive. Now, look carefully at the way the answer choices are worded. Choice (A) is correct because it says the entire country is active, which is the same as saying 0% are inactive. Choice B says the entire country is inactive, which means 100% is inactive (not 0% inactive).

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