Question

Which of the following equations represents a perpendicular line to 6x - 2y = 20?

Answer 1

You have not yet posted the choices.
The perpendicular line has the coefficients of x and y switched, and the sign of ONE of them switched, such as:
2x+6y=40
The 40 could be replaced by any other constant.

Answer 2

y = 3x + 2

y = -3x + 4

y=1/3x-3

y=-1/3x-5

Answer 3

Compare the choices with the transformed version of
6x - 2y = 20
to
y=3x-20 (slope = 3)
you look for the equation whose slope multiplied by (3) equals -1, i.e.
look for the equation whose slope is -1/3.