How can you determine if a slope is undefined?

A slope is considered undefined when it is associated with a vertical line. This means the line does not run horizontally at all; instead, it rises or falls straight up and down. In terms of mathematics, the slope is calculated as the rise over the run (change in y divided by change in x). For vertical lines, the run is zero because the x-coordinates do not change; this results in division by zero, which is mathematically undefined.

Thus, when determining if a slope is undefined, observing that the line is vertical is key. In contrast, horizontal lines have a slope of zero, while a line that forms a right angle does not inherently possess a defined slope unless more context about the specific angles is provided. A vague notion that a slope "has no value" may mislead without a precise definition; in general terms, an undefined slope clearly corresponds to vertical lines due to the mathematical nature of zero in the denominator.