Slope

Have you ever noticed that some roads are easier to drive on than others? One reason may be steepness, which engineers consider when designing roads.

If a road is too steep, some vehicles may struggle to climb it, and drivers may struggle to brake on the way down. To measure and compare this steepness, we use slope.

To find a road’s slope, we select two points on the road. The difference in height between the points is the rise, and the horizontal distance between them is the run. We calculate the slope by dividing the rise by the run.

On a coordinate graph, this road section can be modeled as a line between two points. Here, the rise is the change in y-values, and the run is the change in x-values. Slope shows how much y changes for each one-unit increase in x. This is called the rate of change.

Besides measuring steepness, slope also shows direction. A line with a positive slope rises from left to right. A line with a negative slope falls from left to right. A line with zero slope is horizontal, and a line with an undefined slope is vertical.

By measuring slope, engineers can compare road designs and help create safer routes.