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.
