Are the two functions parallel, perpendicular, the same equation, or none of these choices? - x-3y = - 18 9x-3y = - 27

They are perpendicular. If you normalize both functions into y=ax + b form, you get:

-x-3y=-18 = > - 3y = - 18+x = > y = 6 - 1/3 x

9x-3y=-27 - > - 3y = - 27-9x = > y = 9 + 3 x

Just comparing the slopes, you see they are - 1/3 and 3, which are each other's negative reciprokes. Negative reciprocal slopes are perpendicular.