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Mathematics > Standard Multiple Choice

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

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In the figure, the slope of the line through points P and Q is three over two. What is the value of k?

Answer Choices

Right-o!

Explanation

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

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