What Is a Linear Equation?

What Is a Linear Equation?

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

An Example of a Linear Equation

An example of a linear equation is shown below:

In this example, there are two variables (x and y).

None of the variables have a number written to the right and above it (that is, the highest exponent is 1).

Interactive Widget

You can use this interactive widget to create a graph of your linear equation. Use the buttons to change the values of the linear equation.

Change the Linear Equation
y+ y-
x+ x-
y-intercept + y-intercept -

Oops, it's broken!

Turn your phone on its side to use this widget.

Linear Equations as Equations of Lines

The linear equation has two variables: x and y.

y equals 2 x plus 1

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

In the table below, pairs of values of x and y are chosen in the left hand column. They are substituted into the equation (y = 2x + 1) in the right hand column. Both sides of the equals sign are equal.

x = 1, y = 3 3 = 2 × 1 + 1 \(\:\:\:\) = 2 + 1 = 3
x = 2, y = 5 5 = 2 × 2 + 1 \(\:\:\:\) = 4 + 1 = 5
x = 3, y = 7 7 = 2 × 3 + 1 \(\:\:\:\) = 6 + 1 = 7

Treat the value of x as the x-coordinate and the value of y as the y-coordinate.

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.

See Also

What are Cartesian coordinates? What is a linear equation (in general form)? What is a linear equation (in slope-intercept form)? What is a linear equation (in slope-point form)?