Are the two lines parallel, perpendicular, or neither?

Question

Are the two given lines parallel , perpendicular, or neither?

a. y= -x+4, y= x+4

b. y= -5, 4x-3y=12

c.  The line that passes through (2,2) and (4,8) and the line 12x-2y=42

Answer 1

a) The slopes (-1 and 1) have turned over fractions (1/1 vs 1/1) and their + - signs are switched, so these lines are perpendicular.

b)

y = 0x - 5

4x - 3y = 12

-3y = -4x + 12

y = (4/3)x - 4

0 and 4/3 are different, so the lines aren't parallel.

0 and 4/3 aren't turned over fractions of each other, so the lines aren't perpendicular.

Answer:  Neither.

c)

(2,2) to (4,8)

slope = (8 - 2) / (4 / 2)

slope = 6/2

slope = 3

12x - 2y = 42

-2y = -12x + 42

y = 6x - 21

The slopes (3 and 6) aren't the same, so the lines aren't parallel.

The slopes aren't fractions turned over of each other, so the lines aren't perpendicular.

Answer:  Neither.