Question

What best describes the relationship between the following two lines?

y = 2x +4
y = –2x +
4
Parallel
Perpendicular
Neither parallel nor perpendicular

Answer 1

Neither parallel nor perpendicular.

Explanation:

y = 2x +4

y = -2x + 4

The 2 slopes are 2 and -2.

If they were equal the 2 lines would be parallel.

If they had the relationship slope1 * slope2 = -1 they would be perpendicular.

They are neither so its the last choice.

Answer 2

Neither parallel nor perpendicular

Explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step 1: Define lines

y = 2x + 4

y = -2x + 4

Parallel lines have the same slope but different y-intercepts. If the 2 lines were parallel, their m value would be the same. If the original line's slope is 2, the parallel line's slope would also be 2. Therefore, they aren't parallel.

Perpendicular lines have the negative reciprocal of the original slope. If the 2 lines were perpendicular, one slope would be 2 and the other slope would be -1/2. Therefore, they aren't perpendicular.

Therefore, our answer is neither parallel nor perpendicular.