Slope is a quantity that measures the steepness of a line. To figure out how to define slope, think about what it means for one line to be steeper than another. Intuitively, one would say the steeper line "climbs faster." To make this mathematically precise, consider the following. If two points on the steeper line that are horizontally one unit apart are compared with two points on the less-steep line that are horizontally one unit apart, the pair on the steeper line will be farther apart vertically. Thus the slope of a line is defined to be the ratio of the vertical distance to the horizontal distance between any two points on that line. Sometimes this ratio is called "rise to run," meaning the vertical change relative to the horizontal change.

Several interesting things can be noticed about the slope of a line. First of all, the definition...