What is undefined slope?

The undefined slope refers to a vertical line on a graph where the slope is not defined. This means that the run between any two points on the line is zero, resulting in a vertical line that goes straight up and down.

When calculating the slope of a vertical line, the formula (y2 - y1) / (x2 - x1) is used, where x2 and x1 are the same value. This results in division by zero, which is mathematically undefined.

In geometry, undefined slope is also associated with the concept of parallel lines. Two lines are parallel if they have the same slope (including undefined slope) and never intersect, indicating that they are always at a constant distance from each other.

In real-world scenarios, a vertical line with an undefined slope can represent situations where there is a sudden and drastic change, such as a vertical drop or rise in elevation. Additionally, undefined slopes are used in engineering and architecture to represent structures that are perfectly vertical, such as walls or columns.