SAT Math Multiple Choice Practice Question 165: Answer and Explanation

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Question: 165

11. In a certain board game, the number of points you earn in each round is a linear function of the number of spaces you control at the end of the round. If you control 3 spaces, you win 10 points. If you control 5 spaces, you win 16 points. If you control 8 spaces, the number of points you win would be

A. 6
B. 22
C. 25
D. 26
E. 160

Correct Answer: C


C. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept. Using x for spaces and y for points, you can find the slope by using the slope formula: . Using this slope and the fact that moving three spaces gives you 10 points, you can write 10 = 3(3) + b, so b = 1. That makes the equation y = 3x + 1, and plugging in 8 gives you 25.

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