PSAT Math Multiple-Choice Question 606: Answer and Explanation

Question: 606

The graph of each equation in the system below is a line in the xy-plane.

y = 6x -2
-6 = 12x -2y

What must be true about these two lines?

• A. The lines are parallel.
• B. The lines are perpendicular.
• C. The lines intersect at .
• D. The lines are the same.

Correct Answer: A

Explanation:

(A) Let's get the second equation in y = mx + b form. First, let's get the y-terms on the left by adding 2y to both sides:

2y - 6 = 12x

Next we need to bring the constant to the right side by adding 6 to both sides:

2y = 12x + 6

Finally, divide both sides by 2:

y = 6x + 3

Comparing the two lines shows they have the same slope but different y-intercepts. Therefore, they are parallel lines, choice (A).

If their slopes had been negative reciprocals of one another, they would have been perpendicular lines.

If the lines had had different slopes, they would have intersected at exactly one point.

If they had had the same slope and the same y-intercept, then they would have been the same line.