1. The phrase "rise over run" refers to the slope of a line, which is usually calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points. 2. To swap the rise and run means to take the reciprocal of the slope. If the original slope is $m = \frac{\text{rise}}{\text{run}}$, then swapping rise and run gives a new slope $m' = \frac{\text{run}}{\text{rise}} = \frac{1}{m}$. 3. This operation effectively turns the slope $m$ into its reciprocal $\frac{1}{m}$. This can be useful in finding the slope of a line perpendicular to the original line (if $m \neq 0$), whose slope is $-\frac{1}{m}$, but here we focus just on swapping rise and run. 4. Summary: Given slope $m = \frac{\Delta y}{\Delta x}$, swapping rise and run means the new slope is $\frac{\Delta x}{\Delta y} = \frac{1}{m}$ assuming $\Delta y \neq 0$.