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.



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Linear Equations as Equations of Lines
The linear equation has two variables: x and y.
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 xcoordinate and the value of y as the ycoordinate.
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:
Forms of Linear Equations
Linear equations come in many forms.

The general form of a linear equation is:

The slopeintercept form of a linear equation is:
m is the slope and c is the yintercept.
Read more about the slopeintercept form of a linear equation

The slopepoint form of a linear equation is:
m is the slope of the line, and the point (x_{1}, y_{1}) is a point (in Cartesian coordinates) on the line.