Inverse variation describes a relationship between two variables in such a way that as one variable increases, the other variable decreases, and vice versa. In mathematical terms, the relationship can be expressed as:
xy = k,
where k is a constant. This means that the product of the two variables is constant. An example of an inverse variation equation could be:
y = &frac{k}{x}
In contrast, direct variation would imply that when one variable increases, the other also increases, typically represented as:
y = kx
To determine if a given equation represents inverse variation, check if it fits the form where the product of the two variables yields a constant. Examples could include equations such as:
- y = 10/x
- xy = 5
Both of these equations illustrate the inverse relationship, indicating that an increase in x results in a decrease in y, supporting the idea of inverse variation.