# Variation

Variation problems involve fairly simple relationships or formulas, involving one variable being equal to one term. Here follows the most common kinds of variation.

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. In the following equation y varies directly with x, and k is called the constant of variation:

$$y=kx$$

Another form of variation is the inverse variation which works when there is a relationship between two variables in which the product is a constant. When one variable increases the other decreases in proportion so that the product is unchanged.

If *y* is inversely proportional to *x and k is a constant*, the equation is of the form :

$$y=\frac{k}{x}$$

When we have a variation where one quantity varies as the product of two or more other quantities we have what is called joint variation:

$$y=kxz$$