What formula is used to calculate the slope of a line between two points?

The formula used to calculate the slope of a line between two points is derived from the definition of slope in a Cartesian coordinate system. Slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). When you have two points, denoted as (x1, y1) and (x2, y2), the slope is calculated by determining the change in the y-coordinates divided by the change in the x-coordinates.

The specific formula, (y2 - y1) / (x2 - x1), effectively captures this concept. Here, (y2 - y1) indicates the vertical change (rise), and (x2 - x1) indicates the horizontal change (run). This ratio tells you how much y changes for a given change in x, which is the definition of slope.

Thus, the correct answer accurately reflects the relationship between the two points and is fundamental in graphing linear equations and understanding their characteristics.