# Linear function

A function is called linear if it consists of a sum of multiples of the variables themselves, possibly plus a constant. For example, $f(x)=3x-2$, $f(x,y)=2x+3y-\frac12$ and $f(x)=4$ are all linear functions, but $f(x)=x^2+x+1$, $f(x)=\frac1x$ and $f(x,y)=xy$ are all non-linear.

A linear function $f(x)$ of one variable can be represented by the straight-line graph $y=f(x)$ (hence the name “linear”), and a linear function $f(x,y)$ of two variables can be represented by the two-dimensional plane $z=f(x,y)$ in three-dimensional space.

See also linear operator for a subtly different use of the term “linear”.