By Charlotte Johnson | Updated August 30, 2022
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The slope of a line represents its steepness—the angle at which it ascends or descends. Expressing slope as a ratio (rise over run) is fundamental in algebra and many applied fields. Understanding how to compute this ratio is essential for students, engineers, architects, and anyone working with geometric data.
Locate two distinct points on the graph. Each point should be written as an ordered pair (x, y). For example, the pair (2, 3) means the point is 2 units along the x‑axis and 3 units up the y‑axis.
Subtract the y‑coordinate of the second point from that of the first point. Using (4, 6) and (3, 2), the rise is 6 – 2 = 4.
Subtract the x‑coordinate of the second point from that of the first. With the same example, the run is 4 – 3 = 1.
Combine the rise and run into a ratio. Here, 4 : 1 indicates that for every 4 units the line ascends, it moves 1 unit horizontally. The same value can be written as the fraction 4/1, simplifying to the numeric slope 4.
