What is the slope of a line that is perpendicular to the line y=1

The slope or a line perpendicular to another line is the negative reciprocal of the first line. Let's say you have a line with slope 6; the slope of the perpendicular line is - 1/6.

Here, we have to use our intuition. A horizontal line has slope 0, and the negative reciprocal of zero is undefined (division by zero). But, thinking visually, you by able to tell that the perpendicular line will be vertical, that is, the line x = a, where a is any number.

The slope of such a line is generally considered undefined or, depending on whom you ask, equal to infinity.