The question is:
What is the equation of a line perpendicular to the x-axis and passes through (3,-2)?
By graphing the line, we know that it is x=3, but how do you find that out without graphing.
You know that a line perpendicular to the x-axis must be vertical and must have an equation of x=something. In the case of (3,-2), it doesn't matter what the Y value is as long as you have the x value and know where on the x-axis the point is, in this case, 3. So the equation will be x=3. If the line were to be horizontal, you would know that the x value must be 0 since it does not intercept the x-axis (there is an exception when the line is on the x-axis though) and the concept would be backwards where it will be y=something.
Sometimes I find it hopeful to draw mental pictures of the situation.
Hope this helps
Derg