Hi Caitlin
Two lines are perpendicular if the product of the slopes is -1. If we rearrange the two equations into the y=mx+b form we can read the slope m as the coefficient of x. So here goes...3x-y=3, add y to both sides 3x=3+y, then subtract 3 from both sides y=3x-3 and the slope m=3. Doing the same kind of rearrangement with the second equation gives y=-(1/3)x-4 so for this line m=-1/3 so the product of the slopes is (-1/3)*3=-1 so the lines are perpendicular.
You can also plot them to demonstrate this property.
Jim
