Expanding on your thought.

1 point can be part of infinite amount of lines with different slopes, and thus 0/0 can equal anything.

And a line with the slope of 1/0 is straight up, and happens to be equal to a line with 2/0. Since all values of y come from the same coefficient, one could say that x/0 equals all numbers.

The problem is it doesn't

It doesn't equal any number. But I still like this way of looking at it.