Question 80519
Find the slope of the line passing through the two points: (3, 4) and (3, -4).

The slope, m is given by:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}}
In this problem:
{{{x[1] = 3}}}
{{{y[1] = 4}}}
{{{x[2] = 3}}}
{{{y[2] = -4}}}
Making the appropriate substitutions, we get:
{{{m = (-4-4)/(3-3)}}}
{{{m = -8/0}}} Undefined! 

The slope is undefined, not 0!
A line with an undefined slope (m = x/0) is a vertical line, which is what you have here.
A line with a zero slope (m = 0) is a horizontal line.