Is y=-3x-8 perpendicular, parallel, or neither?

Y=-3x+8 is not parallel nor perpendicular to y=3x+8.
Thus, it is neither.
If one line is parallel to another line, then they will both have the same slope (the coefficient next to the x).
For instance, y=5x+8 is parallel to y=5x-4.
If one line is perpendicular to another line, then the slopes must be  negative reciprocals of one another (reciprocals multiply together and yield one, like 1/3 and 3.)
A parallel line to y=-3x-8 would be y=-3x
A perpendicular line to y=-3x-8 would be y=1/3x
Since the line we are comparing y=-3x-8 to, which is y=3x+8, meets neither of the constraints for being parallel or perpendicular, the correct answer is neither.