In geometry, a linear function is a function of the form y = m x + b. In calculus, a linear function is a function whose graph is a straight line. In linear algebra, a linear function is a function that satisies f(x + y) = f(x) + f(y) and f(a x) = a f(x).

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A linear function in one variable x therefore has the form f(x) = a x + b, while a linear function in n variables has the form f(x_1, ..., x_n) = b + a_1 x_1 + ... + a_n x_n.

bilinear function | function | line | linear functional | piecewise linear function | polynomial function | vector space

high school level