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What Is a Linear Equation? (Mathematics Lesson)

What Is a Linear Equation?

A linear equation is an equation that shows a straight line when it is plotted.

Real Examples of Linear Equations

Some examples of linear equations are shown below:

Examples of linear equations

Linear Equations as Equations of Lines

A linear equation will often have two variables, x and y.

y equals 2 x plus 1

Certain values of x and y will make both sides of the equation equal.

x = 1, y = 3 (3 = 2 × 1 + 1)

x = 2, y = 5 (5 = 2 × 2 + 1)

x = 3, y = 7 (7 = 3 × 2 + 1)

These pair of x and y values can be plotted on a graph as Cartesian coordinates (x, y). When they are plotted, they make a line:

linear equation as a line

Forms of Linear Equations

Linear equations come in many forms.

The main thing that makes an equation linear is that the variables (x and y) do not have any exponents (see Note).

Curriculum
Algebra Lessons
Interactive Widget
Here is an interactive widget to help you learn about linear equations.
Interactive Test
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Here's a second test on linear equations.
Here's a third test on linear equations.

Note

Understanding What a Linear Equation Is...

Let's see what parts a linear equation can have:

What makes a linear equations

A linear equation can contain:

...And What It Isn't

Now let's see what a linear equation cannot have. If you see any of these, it isn't a linear equation.

What does not make a linear equation

The variables in the linear equation (the y and x) cannot contain:

  • Exponents - variables can only appear as x and y, not as x2 or y3

  • Roots - variables cannot appear as √x or ∛y