PSAT Math Multiple-Choice Question 30: Answer and Explanation

Question: 30

The graph of a line is shown in the xy-plane above. It contains the points (3a, a) and , where a is a positive constant. Which of the following could be the equation of this line?

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

Correct Answer: A

Explanation:

A

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 -2, so the y-intercept is -2. The answers are all in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Eliminate (B) which has a y-intercept of 2. Next, calculate the slope of the line with two points on the line. The given points are all in terms of a, so that variable will cancel out when the points are put into the slop formula: . The slope becomes . Cancel the a in the numerator with the a in the denominator, then multiply the numerator and denominator by 2 to get rid of the fraction in the denominator. The resulting slope is . Eliminate (C) and (D) because they do not have this slope. The correct answer is (A).