Directly Proportional vs. Inversely Proportional

jamesford
Mon, 29 Dec 2008 17:39:09 +0000

AoPS if you have it explains this concept pretty well.

For example, the number of eggs that hens lay is directly proportional to number of hens

e/h = k, where k is a constant.

Think about it. If the farmer needs more eggs, he needs to buy more hens. If e (the numerator) gets bigger, the denominator (h) must also to maintain a constant value. You can also represent direct variation with e = kh. If h goes up, so must e, and vice versa.

Inverse variation is the opposite. If one factor goes up, the other must go down. Say the area of a rectangular coffee table must remain A square units. The formula for the table’s area is thus lw = A. If l is increased, w must decrease in order to maintain a constant area. In other words, l = A/w. If w, the denominator, gets bigger, the quotient gets smaller and thus l gets smaller. If w gets smaller, the quotient gets bigger and thus l gets bigger.