In the slope formula, what does 'rise/run' represent?

The correct choice describes the fundamental concept behind the slope of a line in a Cartesian coordinate system. The phrase "rise/run" specifically denotes the slope of a line, which is 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.

This relationship provides a clear understanding of how steep a line is; for instance, if a line rises significantly while only running a short distance, it has a steep slope. Conversely, if it rises gently over a longer horizontal distance, the slope is shallower. Essentially, it articulates the rate of change between two variables, which is critical not only in mathematics but also in real-world applications such as physics and economics where understanding relationships between changing quantities is essential.

The other options provided do not accurately convey the concept of the slope. While distance between two points might relate to the actual measurement between points on a graph, it does not capture the essence of how slope quantifies a relationship between changes in vertical and horizontal distances. The area of a triangle and the height of a rectangle are geometric concepts unrelated to the interpretation of slope in coordinate geometry.