Question

Which pair of lines are perpendicular

A) y=2x-1 and 2y=-x+3
B) y=3x+4 and 3y-x=5
C) y=-4x+2 and x+4y=6
D) y=-6x-3 and 6x-y=4

Answer 1

Two lines are perpendicular if their slopes multiply to -1. That means we have to look at each individual answer and see if the slopes multiply to -1.

y = 2x - 1 has a slope of 2

2y = -x + 3

y = -1/2x + 3 This has a slope of -1/2.

2 * -1/2 = -1.

Since the slopes of these lines multiply to -1, the answer is A. Since we have our answer, we don't have to do anything else.

Answer 2

The answer is A. A perpendicular equation will have the opposite and reciprocal slope as the original equation.

Once converted to the slope-intercept form of y = mx+b, we find the two equations for A are y = 2x-1 and y = (-1/2)x + 3/2. The opposite reciprocal of the first equation's slope (m in the equation form given) is -1/2, which as you can see if the slope of the other equation.