Which two of these lines are parallel and why: 2x-8y=-24, 4x+y=-2, and x-4y=4

Question

In Algebra

Answer 1

We know that parallel lines have equal slope.

Let's we check now which two of these parallel lines.

Given first line 2x-8y = -24

Subtract 2x from each side.

2x-2x-8y = -2x-24

-8y =-2x-24

Divide to each side by negitive 8.

y = (1/4)x+3

m = 1/4

Second line 4x+y = -2

Subtract 4x from each side.

4x-4x+y = -2-4x

y = -4x-2

m = -4

Third line equation x-4y = 4

Subtract x from each side.

x-x-4y = -x+4

-4y = -x+4

Divide to each side by negitive 4.

-4y/-4 = (-x+4)/-4

y = (1/4)x-1

m = 1/4

First and third line slopes are equal.

So the parallel lines are 2x-8y = -24 and x-4y = 4.