PSAT Math Multiple-Choice Question 28: Answer and Explanation

Question: 28

Which of the following could be the equation of the line in the graph above?

• A. 2y - x = -8
• B. 4y + x = -8
• C. 8y - 3x = 8
• D. 8y + x = 8

Correct Answer: D

Explanation:

D

The question asks for an equation that represents a graph. To find the best equation, compare features of the graph to the answer choices. In the line shown, the point at which the line crosses the y-axis is 1, so the y-intercept is 1. Use the two points on the line, (0, 1) and (8, 0), to calculate the slope: . The correct answer must be the equation of a line with a slope of - and a y-intercept of 1. Rewrite the answers in the slope-intercept form of the equation, y = mx + b, where m is the slope of the line and b is the y-intercept. In (A), the equation becomes 2y = x - 8, or y = x - 4. The slope of this line is , and the y-intercept is -4, so eliminate (A). In (B), the equation becomes 4y = -x - 8, or y = -x - 2. The slope of this line is -, and the y-intercept is -2, so eliminate (B). In (C), the equation becomes 8y = 3x + 8, or y = x + 1. The slope of this line is , and the y intercept is 1, so eliminate (C). In (D), the equation becomes 8y = -x + 8, or y = - x + 1. The slope of this line is -, and the y-intercept is 1, which is the same as the slope and y-intercept of the line shown in the graph. The correct answer is (D).