What is the equation of a vertical line passing through the point (3,-5)
y=-5
x= -5
y= 3
x= 3

A vertical line is described by the x-coordinate only.  There is no slope involved.  (the slope of a vertical line is undefined.)
For example,
The vertical line that passes through the point (5,2) is x=5, because all points x=5 passes through all points of the form (5,k), where k is any real number.