What is the rise over run formula for calculating slope?

The rise over run formula for calculating slope fundamentally represents the change in the vertical direction (rise) divided by the change in the horizontal direction (run) between two points on a graph. In the context of the points represented as (x1, y1) and (x2, y2), the slope is derived from the differences in their y-values and x-values.

The formula for slope is typically defined as the difference in y-values divided by the difference in x-values, which leads to the formulation of (y2 - y1) for the rise and (x2 - x1) for the run. This means that option B correctly describes the formula as it captures the necessary changes in values between the two points:

[ \text{slope} = \frac{y2 - y1}{x2 - x1} ]

This direct relationship clearly shows how steep the line is, indicating that for every unit increase in x, how much y increases or decreases. Such clarity is vital in understanding linear relationships in coordinate geometry as well as in the application of slopes in various mathematical contexts.

Other options do not correctly reflect the conventional understanding of calculating slope. For example, using subtraction in the wrong order or including summation instead of proper