What describes perpendicular lines regarding their slopes?

Perpendicular lines intersect at a right angle, and an essential characteristic of their slopes demonstrates this geometric relationship. Specifically, the slopes of two perpendicular lines are defined as opposite reciprocals of each other. This means that if one line has a slope of (m), the slope of a line that is perpendicular to it will be (-\frac{1}{m}).

For instance, if one line has a slope of 2, a line that is perpendicular to it would have a slope of (-\frac{1}{2}). This reciprocal nature ensures that the product of their slopes equals -1, which is a fundamental criterion for perpendicularity in a Cartesian plane.

Understanding this concept is crucial in geometry and algebra, especially in the context of graphing and equations of lines. The concept of opposite reciprocals allows for the determination of relationships between lines, which can be applied in various mathematical problems and real-world situations.