Slope
Main Concept
The slope of a line through two points x1,y1 and x2,y2 is the ratio of the change in the y-coordinates to the change in the x-coordinates: y2−y1x2−x1.
The phrase rise over run is often used to describe slope, reflecting the common interpretation of the y-coordinate as representing elevation and the x-coordinate as representing (horizontal) distance. Slope is frequently (but not exclusively) denoted by the letter m.
Note:
The slope of a line does not depend on which points on the line are chosen to compute it.
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 (∞).
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 x-coordinates (the run), the change in the y-coordinates (the rise), and the slope of the line are displayed.
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