PSAT Math Multiple-Choice Question 108: Answer and Explanation

Question: 108

A line is graphed in the xy-plane. If the line has an x-intercept of 4 and contains the point (-2, 6), which of the following cannot be true?

• A. The point (-10, -6) is on the line.
• B. The slope of the line is negative.
• C. The y-intercept is positive.
• D. The point (10, -6) is on the line.

Correct Answer: A

Explanation:

A

The question asks for a statement that cannot be true about a graph. When given a description of a graph, make a sketch of the graph and use it to eliminate answers. This line crosses the x-axis at 4, so it contains the point (4, 0) as well as the given point (-2, 6). Draw the graph with these points, and then connect them like this:

Now mark each answer as true or false. The slope and the y-intercept are easy to see, so start with those. The slope is negative, so (B) is true, and the y-intercept is positive, so (C) is true. The question asks for a statement that cannot be true, so eliminate (B) and (C). Choice (A) contains a point in the lower left quadrant of the graph, and (D) contains a point in the lower right quadrant. Since the line goes through only the lower right quadrant, only (D) can possibly be true. Eliminate (D). The correct answer is (A).