Most of us are familiar with the concepts of parallel and perpendicular lines. These phenomena have crucial relevance for our study of the concept of a slope. In the case of parallel lines, two parallel lines will always have equal scope. Things get a little stranger in the case of perpendicular lines, however. In these cases, each line is the negative reciprocal of the other. For example, if one of the lines in our latter case is 4/3, the other is -3/4. If one is 2/8, the other is -8/2. If one is 9/2, the other is -2/9. Keep in mind that this is no less the case with ordinary looking integers. The reason for this is that integers can be written as fractions. Therefore, in the case of an integer like 8, the negative reciprocal of the number is -1/8. The negative reciprocal of 4 is -1/4. The negative reciprocal of 1/6, on the other hand, can be written either -6 or -6/1, both of which mean the same thing.
March 31, 2014