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≠ 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, - 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, - 5
Linear Term	A term that contains exactly one variable whose exponent is 1.	x, - 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
-5y+1	2xy-3
3x-1/2y+2	1/x-2
π 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. 3x + 4 -2x + 9 - x = 13 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.