A linear term is an algebraic expression that includes a coefficient multiplied by a variable with an exponent of one. A linear expression is an expression that includes at least one linear term and any constant terms. No other type of terms may be included. The most common form of a linear expression is given below.

In this expression, $a$ and $b$ are real numbers, with $a\ne 0.$ To completely understand the definition of a linear expression, some important concepts will be be broken down. Consider the example linear expression $x-5y+2.$

$x-5y+2$
Concept	Explanation	Example
Term	Parts of an expression separated by a $+$ or $-$ sign.	$x,$ $\text{-}5y,$ $2$
Coefficient	A constant that multiplies a variable. If a coefficient is $1,$ it does not need to be written due to the Identity Property of Multiplication.	$1,$ $\text{-}5$
Linear Term	A term that contains exactly one variable whose exponent is $1.$	$x,$ $\text{-}5y$
Constant Term	A term that contains no variables. It consists only of a number with its corresponding sign.	$2$

The following table shows some examples of linear and non-linear expressions.

Linear Expressions	Non-linear Expressions
$3x$	$5$
$\text{-}5y+1$	$2xy-3$
$3x-\frac{1}{2}y+2$	$\frac{1}{x}-2$
$\pi x+6y$	$5x^2+x-1$

It is important to keep in mind that before classifying an expression, it must be written in simplest form. The expression $3x+4-2x+9-x$ looks like a linear expression, but the result after simplifying is $13,$ which is a constant and therefore not a linear expression.