What is the rise over the run of a graph?

The rise over the run of a graph refers to the slope of a line, calculated by taking the vertical change (rise) between two points on the line and dividing it by the horizontal change (run) between those same two points. Mathematically, it's expressed as ( \text{slope} = \frac{\text{rise}}{\text{run}} ). A positive slope indicates the line rises as it moves from left to right, while a negative slope indicates it falls. This concept is fundamental in understanding the behavior of linear relationships in graphs.