We can sometimes represent functions with equations. For example, the area, $A$, of a circle is a function of the radius, $r$, and we can express this with this equation: $\displaystyle A=\pi r^2$

We can also draw a diagram to represent this function:

In this case, we think of the radius, $r$, as the input and the area of the circle, $A$, as the output. For example, if the input is a radius of 10 cm, then the output is an area of $100\pi$ cm², or about 314 cm². Because this is a function, we can find the area, $A$, for any given radius, $r$.

Since $r$ is the input, we say that it is the independent variable, and since $A$ is the output, we say that it is the dependent variable.

We sometimes get to choose which variable is the independent variable in the equation. For example, if we know that

$\displaystyle 10A-4B=120$

then we can think of $A$ as a function of $B$ and write

$\displaystyle A=0.4B+12$

or we can think of $B$ as a function of $A$ and write

$\displaystyle B=2.5A-30$