LINEAR FUNCTION

In mathematics, the term 'linear function' can refer to either of two different but related concepts.

Contents

Usage in elementary mathematics

Usage in advanced mathematics

External links

Usage in elementary mathematics

In elementary algebra and analytic geometry, the term ''linear function'' is often used to mean a first degree polynomial function of one variable. These functions are called "linear" because they are precisely the functions whose graph in the Cartesian coordinate plane is a straight line.
Such a function can be written as
: $f(x)\; =\; mx\; +\; b$,
where $m$ and $b$ are real constants and $x$ is a real variable. The constant $m$ is often called the slope while $b$ is the y-intercept, which gives the point of intersection between the graph of the function and the $y$-axis. Changing $m$ makes the line steeper or shallower, while changing $b$ moves the line up or down.

Examples of functions whose graph is a line include the following:

★ $f\_\{1\}(x)\; =\; 2x+1$

★ $f\_\{2\}(x)\; =\; x/2+1$

★ $f\_\{3\}(x)\; =\; x/2-1$
The graphs of these are shown in the image at right.

Usage in advanced mathematics

In advanced mathematics, a ''linear function'' often means a function that is a linear map, that is, a map between two vector spaces that preserves vector addition and scalar multiplication.
A function $f(x)\; =\; mx\; +\; b$ is a linear map if and only if $b\; =\; 0$. For other values of $b$ this falls in the more general class of affine maps.

External links

★ Linear function - Easy math

★ Linear Functions on Id Mind