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Linear Term
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Linear Expression

A linear expression is a type of algebraic expression that contains at least one linear term with a non-zero coefficient. A linear expression may also contain constant terms. No other type of terms may be included. Below is written the most common form of a linear expression.
Parts of the linear expression ax+b

In the above expression, a and b are real numbers, with a0. To completely understand the definition of a linear expression, some important concepts will be be broken down.

Example Linear Expression: x5y+2
Concept Explanation Example
Term Parts of an expression separated by a + or sign. x, -5y, 2
Coefficient Each 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

It is important to keep in mind that before classifying a term, it must be written in simplest form first. The following table shows some examples of linear and non-linear expressions.

Linear Expressions Non-linear Expressions
3x 5
-5y+1 2xy3