Find an equation of the line that has a y intercept of -2 and is perpendicular to the graph of the line x - 2y = 5 ?

First, you'd get x-2y=5 into y=mx+b form. Which would be done like this:
-2y=-x+5 (subtract x in order to get it to the other side
-2y/-2=-x/-2+5/-2 (Divide everything by -2 in order to isolate y)
y=1/2x+-5/2 
Once you're done with that, you just have to replace the y-intercept, and find the negative reciprocal of our slope (1/2), which would be -2
This then makes your answer
y=-2x-2