PSAT Math Multiple-Choice Question 548: Answer and Explanation

Question: 548

Ms. Burke is growing tomatoes on a vine. She plants a starter plant with a height of 6 inches and estimates the height of the vine after each day for 6 days, as shown in the table below.

Height of Vine after Each Day of Growth

Day (x)	Height of Vine (y)
1	7.5 in
2	9.0 in
3	10.5 in
4	12.0 in
5	13.5 in
6	15.0 in

If the line passing through the points defined in the table is graphed on an xy-plane, which of the following is the best interpretation of the slope in the context of the problem?

• A. The amount that the height of the vine is increasing each day
• B. The height of the vine after the seventh day of growth
• C. The height of the vine when it was first planted
• D. The number of days for which the height of the tomato plant will increase

Correct Answer: A

Explanation:

A

The question asks for the best interpretation of the slope of a line representing a set of data. In this question, y represents the height of a vine, and x represents the number of days since the vine was planted. The slope of a graph is defined as the change in y over the change in x, so the slope must relate to height as it increases over time. Eliminate (B) and (C), as they reference the height on specific days. Eliminate (D), as x itself represents days, so the slope cannot also be the number of days. Another way to approach this is to plug and play to see what gives a value that matches the value of the slope. Slope is calculated using the equation slope = . Calculate the slope of the line using two points, such as (1, 7.5) and (2, 9.0). The slope formula becomes . Choice (A) refers to the amount that the height of the vine is increasing each day. Each day, the vine's height increases by 1.5 inches. Keep (A), but check the remaining answer choices just in case. Choice (B) refers to the height of the vine after the seventh day of growth. The vine grows 1.5 inches each day, so the vine will be 15.0 + 1.5 = 16.5 inches on the seventh day. Eliminate (B), as this does not match the value of 1.5 inches. Choice (C) refers to the height of the vine when it was first planted. The question states that the starter plant had a height of 6 inches. Since the vine's height when planted is not 1.5 inches, eliminate (C). Choice (D) refers to the number of days the plant will keep growing, but no information is given about how long the plant will grow. Either way, the correct answer is (A).