Slope - Definition


The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. This is described by the following equation:

(The Greek letter delta "Δ", is commonly used in mathematics to mean "difference" or "change".)

Given two points (x1,y1) and (x2,y2), the change in x from one to the other is x2x1 (run), while the change in y is y2y1 (rise). Substituting both quantities into the above equation generates the formula:

The formula fails for a vertical line, parallel to the y axis (see Division by zero), where the slope can be taken as infinite, so the slope of a vertical line is considered undefined.

Read more about this topic:  Slope

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