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

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

1. 4
2. 5
3. 6
4. 7
5. 8

Correct Answer: B

Here's Why:

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

Difficulty: Medium

Question Type: Standard Multiple Choice