X doesn't have to equal to 4, it can be equal to any real number really (as in, not i), the really important part is that Y is equal to both Positive and Negative Infinity, just like in a horizontal line Y can be equal to any real number, but, in this case, X has to be equal to both Positive and Negative Infinity.
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No, it is horizontal.
That would be because all the graphed values of x are 4. So you can plug anything in for Y and it will still be on that vertical line.
The line x = -4 is vertical, so a line that is perpendicular to it is horizontal, so its slope is 0.
a vertical line at x=3
That's a vertical line; the slope is not defined.