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What Is the Definition of a Linear Expression?

linear expression: equations on a grid paper

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

Note that the coefficients in front of the variables don't matter. Let's take a couple of these polynomials (a polynomial just means an expression with two or more terms) as examples.

2x - y + 3 is a linear expression.

x + y + z⁵ is a non-linear expression. It contains a term raised to the fifth power.

4 - 2 is a linear expression.

Linear Expressions vs Linear Equations

The main difference between a linear expression and a linear equation is that the linear equation has an equal sign in the expression.

In the common core, you learn that a linear equation is the same thing as a linear function.

Graphing linear equations relates the y-coordinate to the x-value according to the computation of the expression.

Let’s take 2x - y + 3 as an example. This is a linear expression. However, if we were to set the expression equal to something, as in 2x - y + 3 = 0, we would get an equation.

There are different equation forms, the two most common being standard form and slope-intercept form. As a review, linear equations always graph to a straight line.

Here is an example of the linear equation above in standard form: 2x - y = -3

Here is the linear equation in slope-intercept form: y = 2x + 3

On the graph, they both become a straight line:

straight line on a graph

Recognizing Linear Expressions

A linear expression is an algebraic expression where each term is either a numeric constant or a variable raised only to the first power. It is most commonly seen in linear equations.

Remember that just as in linear equations, coefficients can be either positive numbers or negative numbers. It’s the exponent that matters. A single variable that is raised to a power greater than 1 will make the whole expression non-linear.

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