# The total population of animals is directly proportional to the size of the habitat (in acres)...

## Question:

The total population of animals is directly proportional to the size of the habitat (in acres) polled. Write an equation using only one variable that could be used to solve for the constant of variation {eq}k {/eq}.

## Directly Proportional

To quantities are directly proportional to each other when they move in the same direction as one changes. For example, we expect that the population will increase as the area available to it increases.

Let the population be p and the size of the habitat be x. Then, as they are directly proportional to each other, we have:

$$p\propto x$$

If we add the constant of variation, we get the equation of one variable that could be solved to find its value.

$$p=kx$$