The form is different for vertical lines than for all other lines.  That's
because the slope of vertical lines is undefined.  Vertical lines are
considered to be "infinitely steep". The equation for a vertical line is done
this way:

Here is the given point the vertical line goes through:



Here is the vertical line:



Now let's look at a whole bunch of other points on that line:



Now let's ask the question:  What is true about every one of those points?

Answer:  Every one of them has its x-coordinate as -4.

Therefore the only equation that tells the whole story of that
vertical line is the statement that means:

   " x is always -4 "

and that is the very simple equation:

        x = -4

So that's all there is to the equation of that vertical line.
Every point on a vertical line has its x-value the same.  In
this case it is -4.  So the equation of that green vertical line is
simply: 

        x = -4

There is no solving needed to get the equation of a vertical line.  It's
just x = ___  where you fill a number in the blank which is the x-coordinate
of any point on the line, since they're all the same.

Edwin