PSAT Math Multiple-Choice Question 522: Answer and Explanation

Question: 522

Which of the following equations is graphed on the xy-plane above?

• A. y = x – 5
• B. y = –x + 5
• C. y = x – 5
• D. y = –x + 5

Correct Answer: A

Explanation:

A

The question asks for an equation that represents a line. To find the best equation, compare features of the line to the answer choices. The graph for this line has a y-intercept of –5 and a positive slope. Eliminate answer choices that do not match this information. The equations are written in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Choices (B) and (D) have negative slopes, so eliminate (B) and (D). Compare the remaining answer choices. Both (A) and (C) have y-intercepts of –5 and positive slopes, so find the slope of the line using two points on the line, such as (6, –1) and (3, –3). Slope is calculated using the equation . The equation becomes . Choice (C) has a slope of , so eliminate (C). Another option would be to pick a point on the graph such as (6, –1) and plug it into the given equations to see if they are true. Either way, the correct answer is (A).