Which formula represents the slope of a line?

The formula representing the slope of a line is derived from the concept of the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. The correct formula, which is represented by the choice selected, states that the slope (m) is equal to the difference in the y-values (y2 - y1) divided by the difference in the x-values (x2 - x1).

This relationship is crucial because it reflects how steep the line is: a larger value indicates a steeper incline, while a smaller value indicates a gentler slope. This formula is essential when analyzing linear graphs, as it allows for the calculation of how much y changes for a unit change in x, enabling further understanding of the relationship between the two variables represented in a coordinate system.

The correct understanding of this formula is fundamental in various applications, including real-world scenarios like determining rates of change or predicting outcomes based on a linear relationship.