In what method is the slope calculated?

The slope of a line or surface is defined as the ratio of the vertical change (rise) to the horizontal change (run). This relationship is crucial in many fields, including surveying, as it helps determine how steep a surface is. In the context of slope calculation, "rise" refers to the difference in height (vertical change) between two points, while "run" is the distance between those two points measured horizontally.

Because slope is fundamentally about understanding how much vertical change occurs relative to horizontal movement, the method of rise over run provides a clear and intuitive way to quantify this relationship. It can be expressed mathematically as:

[ \text{slope} = \frac{\text{rise}}{\text{run}} ]

This formula is particularly relevant in surveying, where accurately calculating slopes can influence construction, land use, and drainage considerations. Other options given do not accurately depict the concept of slope:

• Height divided by width does not specifically capture the rise versus run relationship.

• Base times height represents an area calculation, not a ratio.

• Length times width, like the previous option, pertains to area and does not relate to slope at all.

Thus, rise over run is the fundamental method for accurately calculating slope in various practical