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

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)