From the graph of x = 4 find the characteristics of the line.

The equation tells us that x always equals 4.  This is a
constraint on the value of x.  However, there are no restrictions on what the value of y
can be, so once one is at 4 on the x-axis (4,0), there is an infinite number of points
both positive and negative which create a line parallel to, and four units to the right
of, the y-axis, a vertical line.

The slope of a vertical
line is UNDEFINED.  Why is that so?  If you have a line with a positive slope, and you
make it steeper and steeper so that the [absolute] value of y is increasingly greater
than the [absolute] value of x, you eventually will approach a limit of positive
infinity.  If you do the same thing with a negatively-sloped line, you eventually will
approach a limit of negative infinity.  A number cannot be infinitely positive and
infinitely negative at the same time, so that is why the slope of a vertical line is
undefined.