a zero denominator means that the line is vertical
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it means the function is undefined at that point
or yes the slope could be seen as a vertical line
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.
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A zero denominator means that the function is undefined. It has no slope.
Which is different from having a slope of zero. Basically dividing by zero is a no-no.
Also a zero denominator shows where a vertical asymptote is defined which is usually referred to as an imaginary vertical line
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)