Slope
Main Concept

The slope of a line through two points $\left({x}_{1}\,{y}_{1}\right)$ and $\left({x}_{2}\,{y}_{2}\right)$ is the ratio of the change in the ycoordinates to the change in the xcoordinates: $\frac{{y}_{2}{y}_{1}}{{x}_{2}{x}_{1}}$.
The phrase rise over run is often used to describe slope, reflecting the common interpretation of the ycoordinate as representing elevation and the xcoordinate as representing (horizontal) distance. Slope is frequently (but not exclusively) denoted by the letter m.
Note:
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The slope of a line does not depend on which points on the line are chosen to compute it.

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The slope of a vertical line is not defined, since the denominator of the calculation would be 0. In some situations, it is reasonable to represent the slope of a vertical line as infinity ($\infty$).

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The slope of a horizontal line is 0.





Visualizing slope


Click or drag in the plot below to draw a segment of a line. The change in the xcoordinates (the run), the change in the ycoordinates (the rise), and the slope of the line are displayed.

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