Determine What the Lines Are?

Question

The equations of two lines are given. Determine if the lines are parallel, perpendicular or neither.

(1) y = (1/2)x - 3 and y = -2x + 4

(2) y = -2x + 3 and y = (-1/2)x + 2

Answer 1

If the lines are written in y = mx + b form (and all 4 of those are), your question can be answered by inspection.

Parallel lines have the same slope.
Perpendicular lines are lines whose slopes multiply to give you -1. (Negative 1)

Neither (1) nor (2) are parallel.
(1) is perpendicular, but (2) is not.

Answer 2

just get the slopes of the line. if the slopes are the same then they are parallel and if they are opposite reciprocals of each other then they are perpendicular.
So for your problem they are neither because -2 does not equal -1/2 nor are -2 and -1/2 opposite reciprocals.
(A negative reciprocal would be -2 and 1/2)

Answer 3

1) slopes are 1/2 and -2, product is -1, perpendicular

2) slopes are -2 and -1/2, product is +1, neither.