slope

Also known as gradient of a line, gradient

right|thumb|Slope: m = \frac{\Delta y}{\Delta x} = \tan(\theta)

AI overview

Slope measures how steep a line is by comparing the vertical change to the horizontal change between two points on that line. It matters because slope helps us understand rates of change in many real-world situations, from the steepness of a hill to how quickly something increases or decreases over time.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

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exact match: purl.obolibrary.org/obo/ENVO_00002000

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~13 min read

Article

14 sections

Contents

Notation
Definition
Examples
Algebra and geometry
Examples
Statistics
Calculus
Difference of slopes
Slope (pitch) of a roof
Slope of a road or railway
Other uses
See also
References
External links

right|thumb|Slope: m = \frac{\Delta y}{\Delta x} = \tan(\theta)

In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same A slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angle for any choice of points. To explain, a slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angle. The line may be physical – as set by a road surveyor, pictorial as in a diagram of a road or roof, or abstract. An application of the mathematical concept is found in the grade or gradient in geography and civil engineering.