Question

Are the given lines parallel, perpendicular, or neither?
3x + 12y = 9
2x - 8y = 4

Answer 1

The line are neither.

Explanation:

2x -8y = 4 subtract 2x from both sides

-8y = -2x + 4 Divide all the way through by -8 and simplify

y =
`(1)/(4)`x -
`(1)/(2)`

3x + 12y = 9 Subtract 3x from both sides

12y = -3x + 9 Divide all the way through by 12 and simplify

y =
`(-1)/(4)`x +
`(3)/(4)`

For the lines to be parallel, the slopes (1/4 and -1/4) need to be the same. They are not. They are opposites of each other.

For the lines to be perpendicular, the slopes (1/4 and -1/4) need to be opposite reciprocals of each other. The opposite reciprocal of 1/4 would be -4,