Inverse variation is a type of proportionality where one quantity decreases while the other increases or vice versa. In other words, two quantities follow inverse variation if one quantity is directly proportional to the reciprocal of the other quantity. This means that an increase in one quantity leads to a decrease in the other while a decrease in one quantity leads to an increase in the other.
Inverse variation can be represented by the equation y=k/x or xy=k, where k is a constant of proportionality. The product rule of inverse variation states that if x1 and y1 are inversely related to x2 and y2, then x1y1=x2y2.
An inverse variation table is used to examine how one quantity changes with a change in another quantity that follows an inverse proportionality. For example, if two quantities x and y are in an inverse variation given by y = 18 / x, then the inverse variation table can be given as follows:
| x | y = 18 / x |
|---|---|
| 1 | 18 |
| 2 | 9 |
| 3 | 6 |
| -3 | -6 |
| -2 | -9 |
| -1 | -18 |
In summary, inverse variation is a type of proportionality where one quantity decreases while the other increases or vice versa. It can be represented by the equation y=k/x or xy=k, and the product rule of inverse variation states that x1y1=x2y2 if x1 and y1 are inversely related to x2 and y2.
