How do you calculate the slope of a line given two points, (x1, y1) and (x2, y2)?

To calculate the slope of a line given two points, (x1, y1) and (x2, y2), the formula involves determining how much the y-values change for a given change in the x-values. The correct formula is the difference in y-values divided by the difference in x-values, which is represented as:

Slope (m) = (y2 - y1) / (x2 - x1)

This definition of slope reflects the concept of rise over run, where "rise" is the change in the vertical direction (from y1 to y2) and "run" is the change in the horizontal direction (from x1 to x2). By applying this calculation, one can understand the steepness and direction of the line formed by the two points.

When comparing this with the other choices, the other formulas do not accurately reflect the relationship between the coordinates needed to find the slope. For instance, the calculation involving addition of the points does not represent any meaningful relationship in slope calculation, and the formulas that suggest swapping x and y differences lead to incorrect interpretations of slope. Thus, the correct approach is clearly followed in the stated formula, making it vital for understanding slope in the context of linear relationships.