Slope
A measure of the steepness or degree of incline of a surface, important in terrain analysis and hydrological modelling.
What does Slope represent?
The rate at which elevation changes over distance is represented by slope in GIS. Usually obtained from a Digital Elevation Model (DEM), it displays the degree of steepness or flatness of the terrain at any particular point on a surface.
Slope measures how much vertical change (rise) occurs for a given horizontal distance (run).
Slope=RiseRun\text{Slope} = \frac{\text{Rise}}{\text{Run}}Slope=RunRise
It is usually expressed in:
Degrees (0° = flat, 90° = vertical)
Percent (e.g., 45% slope = 45 meters rise per 100 meters run)
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In mathematics, the slope of a line measures its steepness and direction. It is calculated using the formula slope (m) = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
A line's slope, which is determined by dividing its vertical change by its horizontal change, indicates how steep it is. Slope can be expressed mathematically as (rise/run) = (y₂ – y₁) / (x₂ – x₁), where (x₁, y₁) and (x₂, y₂) are two locations on the line.
A line or surface's slope is a measurement of its steepness. It shows the ratio of the horizontal change (run) to the vertical change (rise) between two points on a line in mathematics. A slope of two, for instance, indicates that the line rises two units for every unit it advances horizontally. In real life, slope might refer to the incline of a roof or the steepness of a hill.
A line's slope in coordinate geometry indicates how steep or inclined it is. It is computed using the formula m = (y₂ – y₁) / (x₂ – x₁), which is the change in the y-coordinate divided by the change in the x-coordinate between two locations on the line. A line with a positive slope climbs from left to right; one with a negative slope falls; one with a zero slope is horizontal; and a line with an indeterminate slope is vertical.