Which line is perpendicular to x= -3 and goes through the point (0, -4) ?
x=0
(y+4)=x
y=x+4
y= -4

X=-3, this is a vertical line at x=-3.  (because for x=-3 is the line with all real values of y, (-oo, +oo).

For lines to be perpendicular, their slope have to be negative reciprocals.  Mathematiclly:

m1*m2=-1

The slope of a vertical is infinite so m2=-1/+oo=0.  Which means that the perpendiular line has a slope of zero, it is a horizontal line.

Since there is a slope of 0, the point slope intercept  form of the lines is:

y=k  where k is the constant that is equal to the y value that the line must pass through, which in this case is -4.  So the perpendicular line is:

y=-4