The slope is represented mathematically as: m =

In the case of a road, the 'rise' is the change in altitude, while the 'run' is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. Slope is essentially the change in height over the change in horizontal distance, and is often referred to as 'rise over run.' It has applications in gradients in geography as well as civil engineering, such as the building of roads.

A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator.

A line has a constant slope, and is horizontal when m = 0.

A line is decreasing, and goes downwards from left to right when m < 0.

A line is increasing, and goes upwards from left to right when m > 0.Given m, it is possible to determine the direction of the line that m describes based on its sign and value: The larger the value is, the steeper the line. Generally, a line's steepness is measured by the absolute value of its slope, m. Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m.

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