Question

what is the negative inverse of the slope 0

Answer 1

since the slope zero is not going anywhere therefore it will only be a point at the origin (0,0) therefore there is no negative inverse of slope 0.

Answer 2

A slope of 0 means you have a horizontal line. It sounds like you're looking for a line perpendicular to it (judging by the "negative inverse" part of your question, which should actually read reciprocal instead of inverse).

Any vertical line is perpendicular to any horizontal line, so the slope is \(\infty\).