Write an equation of the line that passes through (-3,4) and is perpendicular to the line y=2x-5.

Answer:
y-y1=2(x-x1)
y-4=2(x+3)

Is this how I would write my equation or should I distribute the 2 to make it y-4=2x+6?

y-4=2(x+3)

is the line parallel to y=2x-5

You want the line perpendicular. So, your equation is

y-4 = -1/2 (x+3)

you can massage that as you will.