What does the slope of a line measure?

The slope of a line measures the steepness of the line. In mathematical terms, it represents the ratio of the vertical change (rise) to the horizontal change (run) between two distinct points on the line. This means that a higher slope value indicates a steeper line, whereas a slope of zero indicates a horizontal line. Additionally, a positive slope suggests that as one variable increases, the other variable also increases, while a negative slope indicates the opposite relationship. Understanding slope is critical in various applications, including physics, economics, and statistics, as it provides insight into the relationship between variables represented graphically.

Other options do not accurately capture what slope represents: length refers to a measure of distance, the angle between intersecting lines relates to geometrical concepts rather than the slope of a single line, and the area under a line typically pertains to integration in calculus rather than the slope itself. Thus, the correct answer aligns directly with the fundamental definition of slope in geometry and algebra.