PSAT Math Multiple-Choice Question 488: Answer and Explanation

Question: 488

Sarah’s parents tracked the amount of time she spent on homework as she grew up. The scatterplot above shows how the amount of time t, in hours, Sarah spent on homework in relation to her age a, in years. Which of the following equations best models this data, where 6 ≤ a ≤ 12?

• A. t = –0.5a – 2.5
• B. t = –2.5a – 0.5
• C. t = 0.5a – 2.5
• D. t = 2.5a – 0.5

Correct Answer: C

Explanation:

C

The question asks for an equation that represents a graph. Pick a point that is on the graph and plug it into the answer choices to see which ones are true. The graph contains the point (7, 1), with 7 on the x-axis, so plug a = 7 and t = 1 into the answers. Eliminate answer choices that contain false equations. Choice (A) becomes 1 = –(0.5)(7) – 2.5, then 1 = –3.5 – 2.5, so 1 = –6. This is not true, so eliminate (A). Choice (B) becomes 1 = –(2.5)(7) – 0.5, then 1 = –17.5 – 0.5, or 1 = –18. Eliminate (B). Choice (C) becomes 1 = (0.5)(7) – 2.5, then 1 = 3.5 – 2.5, or 1 = 1. This is true, so keep (C), but check (D) just in case. Choice (D) becomes 1 = (2.5)(7) – 0.5, then 1 = 17.5 – 2.5, or 1 = 15. Eliminate (D). The correct answer is (C).