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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The slope of a line passing through the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is the ratio of the vertical change $(Δy)$ to the horizontal change $(Δx)$ between the points. The variable $m$ is most commonly used to represent slope.

$m=ΔxΔy $

The words *rise* and *run* are sometimes used to describe the slope of a line, especially when the line is given graphically. Rise corresponds to $Δy$ and run corresponds to $Δx.$

This gives the following definition for the slope of a line.

$m=ΔxΔy =runrise $

The sign (positive or negative) of each distance corresponds to the direction of the movement between points. Moving to the right, the run is positive; moving to the left, the run is negative. Similarly, moving up yields a positive rise while moving down gives a negative rise.