Perpendicular and parallel lines

Question

I recently did a test and did horrid i was jusf hoping you can explain what i did wrong. So the question states, which of these is an equation of a line that is parallel to line a? Choose all that apply. Line A can be described by the equation 3x-4y=8 And the choices were

A. -3x-4y=6

B. -3x +4y=6

C. 3x -4y = 6

D. 3x+4y=6

So what would be the answer and how would i solve that?

Thank you so much.

Answer 1

As these are all written in the same form, no reason to explicitly determine the slope.

The original equation is 3x - 4y = 8

Clearly , 3x - 4y = 6 is parallel, as the numbers on the left side are the same, we just have a different value on the right side.

Note, though, that -3x + 4y = 6 may be rewritten as 3x - 4y = -6, so it is also parallel.

If the coefficients are a multiple of 3 and -4 (the one that I switched could be viewed as a multiple of -1), it will be parallel.