Question

Determine whether each pair of lines is parallel, perpendicular, or neither.

x - 4y= -4
y = 4x-4
Choose the correct answer below.

A: perpendicular
B: parallel
C: neither

Just wanted to make sure if I was correct

Answer 1

neither

Explanation:

• Parallel lines have equal slopes

• the product of the slopes of perpendicular lines = - 1

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

x - 4y = - 4 ( subtract x from both sides )

- 4y = - x - 4 ( divide through by - 4 )

y =
`(1)/(4)` x + 1 ← in slope- intercept form

with slope m =
`(1)/(4)`

y = 4x - 4 ← is in slope- intercept form

with slope m = 4

clearly the lines are not parallel and
`(1)/(4)` × 4 = 1 ≠ - 1

thus the 2 lines are neither parallel nor perpendicular