The slope is defined as
[tex] m = \dfrac{\Delta y}{\Delta x} [/tex]
which means that you have the difference of the y coordinates of the two points at the numerator, and the difference of the x coordinates of the two points at the denominator.
So, if the two points have the same x coordinate, the denominator vanished, and the slope is not defined.
Since the only points with the same x coordinate are those in option c, that is the correct answer.
