The slope of a line corresponds to the idea of the steepness of an inclined plane or the steepness of a stairway. If all the steps of a stairway are uniform, the steepness of the stairway can be defined in terms of the "rise" and "run" of one of the steps. The steepness of a uniform stairway is the number obtained by dividing the rise by the run of one of the steps. If the rise (vertical component) is 6 inches and the run (horizontal component) is 8 inches, then the steepness of the stairway is 6/8 (or 3/4). Likewise, in formal geometry, slope, in rectangular coordinates, is defined as the ratio of the change of the ordinate (vertical component) to the corresponding change of the abscissa (horizontal component) of a point moving along a nonvertical line.

The origin of the term slope as used in mathematics most likely came from the...