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
None of the variables have a number written to the right and above it (that is, the highest exponent
Linear Equations as Equations of Lines
The linear equation has two variables: x
Pairs of values of x
will make both sides of the equation equal.
In the table below, pairs of values of x
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
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
...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
Exponents - variables can only appear as x and y, not as x2 or y3
Roots - variables cannot appear as √x or ∛y