American Institute of Certified Planners (AICP) Practice Exam

How is the slope defined in terms of elevation?

1. Elevation change multiplied by horizontal distance

2. Change in elevation divided by horizontal distance

3. A constant rate of 1:1 ratio

4. Vertical distance without relation to horizontal distance

The correct answer is: Change in elevation divided by horizontal distance

The definition of slope in terms of elevation is expressed as the change in elevation divided by the horizontal distance. This relationship quantifies how steep a surface is by comparing the vertical change (rise) to the horizontal distance (run). Therefore, if you have a point that is higher or lower than another point, the slope can articulate how quickly or gradually the elevation changes over a specific distance in a horizontal direction. The concept behind this is fundamental in various fields, including geography, engineering, and urban planning. A slope of 1:1, which might imply a consistent rise over a particular horizontal distance, does not accurately reflect the calculation of slope as a ratio of change but rather describes a specific inclination. This means it doesn't account for varying distances or elevation changes. Defining slope in a manner that isolates vertical distance without considering horizontal distance does not provide a complete understanding of the slope’s nature, as slope inherently involves the relationship between both dimensions. In short, the ratio established by dividing the change in elevation by the horizontal distance offers the most comprehensive and correct method for defining slope in terrain and planning contexts.