Find the value of constant n if the lines y=(n-2)x+12 and 3x-4y+5=0 are:

Question

a) parallel and
b) perpendicular to each other.

Thanks in advance.

Answer 1

Parallel lines have the same slope so the slope of 3x-4y+5 =0 is y=(-3x-5)/-4 slope =3/4
therefore the y=(n-2)x+12 must have a slope of 3/4
so n-2=3/4
n=2.75
If the lines are perpendicular they have negative reciprocal slopes therefore n-2= -4/3
n=2-4/3 or 2/3