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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In the figure, the slope of the line through points P and Q is 3/2. What is the value of k?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

答案和解析

答案：B

解析：

The slope of a line in a coordinate plane is given by the fraction whose numerator is the change in y between any two points on the line and whose denominator is the change in x between the same points on the line.

The question asks for the value of k, which is the x-coordinate of point Q .

The change in ybetween points P and Q is 7-1 = 6. The change in x between these points is k-1. Since the slope is 3/2, it follows that 6/(k-1) = 3/2. Solving this equation gives (3k)-3 = 12. Therefore, 3k = 15, and k = 5.