Question

a zero denominator means that the line is vertical

Answer 1

it means the function is undefined at that point

Answer 2

or yes the slope could be seen as a vertical line

Answer 3

The result of dividing through zero can not be defined consistently. A vertical line is not the graph of any function. So you can not talk about slope.

Answer 4

A zero denominator means that the function is undefined. It has no slope.

Answer 5

Which is different from having a slope of zero. Basically dividing by zero is a no-no.

Answer 6

Also a zero denominator shows where a vertical asymptote is defined which is usually referred to as an imaginary vertical line

Answer 7

This statement lacks mathematical rigour. First of all a vertical asymptote is not part of the function. Also not everywhere where there occurs a zero denominator there has to be a vertical asymptote (see x/x for example which can be extended continuously in zero) and not everywhere where there is a vertical asymptote, do you have a zero denominator. (take ln x for example with a vertical asymptote at x = 0)