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Linear Function

Basic definitions

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).

Detailed definition

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.

Educational grade level

high school level

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