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Linear Expression

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.
The linear expression ax+b, where a is the coefficient, x is the variable, ax is the linear term, and b is the constant term.

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

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

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

Linear Expressions Non-linear Expressions
It is important to keep in mind that before classifying an expression, it must be written in simplest form.
The expression looks like a linear expression, but the result after simplifying is which is a constant and therefore not a linear expression.