How can I Find the equation of the line passing through(2,-4) and perpendicular to y=-3

Question

Please provide me with the details on how to proceed with this problem

Answer 1

The line y=-3 is horizontal.  So, the perpendicular line is vertical.

 

Every point on a vertical line has the same x-coordinate.  Since (2,-4) is on the line, all the x-coordinates of the points on the line must be 2 as well.  

 

So, the equation of the line is:  x = 2.

Answer 2

Perpendicular to a horizontal line (y=-3) is a vertical line, so x=c.

Going through (2,-4) means (2,-4) must satisfy x=c so 2=c so x=2.