PSAT Math Multiple-Choice Question 127: Answer and Explanation

Question: 127

The two equations in the system of equations above each form a line when graphed in the xy-plane. Which of the following statements is true regarding these two lines?

• A. The lines are the same line.
• B. The lines are perpendicular.
• C. The lines are parallel.
• D. The lines intersect at (3, 2).

Correct Answer: B

Explanation:

B

The question asks for a true statement given the equations of two lines. Choices (A), (B), and (C) state that the lines are the same line, perpendicular, or parallel, respectively. To determine whether any of these is true, find the slopes of the two lines. The first equation is in standard form: Ax + By = C. The slope of a line in standard form is . For this equation, A = 3 and B = 2, so the slope of this line is . The second equation is in slope-intercept form: y = mx + b. The slope of a line in slope-intercept form is m, so the slope of the line is . The two slopes are negative reciprocals, which means the lines are perpendicular. The correct answer is (B).