Question

Which equation represents a line which is perpendicular to the line 5x+6y=−42?

Answer 1

First we bring the line into standard form:
5x+6y=-42
6y=-5x-42
y=(-5/6)x-7

the line has a slope m=-5/6
to get the slope of a perpendicular line you have to know that for slopes of two perpendicular lines this relationship holdes:
m1*m2=-1
if we insert the slope:
-5/6*m2=-1
m2=-1/(-5/6)
m2=-6/-5=6/5

-> y=6/5x
this passes though (0,0)