The Lesson
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).
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.
What a Linear Equation Is...
Let's see what parts a linear equation can have:
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.
The variables in the linear equation (the
y and
x)
cannot contain:

Exponents  variables can only appear as x and y, not as x^{2} or y^{3}

Roots  variables cannot appear as √x or ∛y