The document defines and provides examples of linear equations. A linear equation is one whose graph forms a straight line. The variables in a linear equation cannot be raised to powers higher than 1 and cannot be multiplied or divided. Examples of linear equations are provided. Methods for determining if a given equation is linear and for proving a linear equation graphs as a straight line using a table of values and graphing are described.

1. Linear Equations
If you recall from previous learning, an equation is a mathematical sentence that
includes an equal sign. A linear equation is an equation whose graph forms a straight line. The
points on the line are all solutions of the equation.
Remember that variables, such as “x” and “y” are letters that represent numbers we
don’t know. Variables are an important part of a linear equation. In fact, there are two variables
in a linear equation. The two variables most often used are “x” and “y”.
In order for an equation to be a linear equation, there are a couple of rules. First, the
variables can’t be raised to a power other than one. Therefore, a linear equation does not have
x2 , y3, etc. If you see a variable with an exponent, it can’t be a linear equation. Another rule is
the variables can’t be multiplied or divided. The following equations are NOT linear equations:
y = x2
3xy = 2
The following ARE examples of linear equations:
y = 2x + 1
2x + 3y = 4
y – x = 1
Tell whether the following equations are linear and explain:
y = 1/2 x + 5
______________________________________________________________________________
3x + 2y = 10
______________________________________________________________________________
y = x2 +2
______________________________________________________________________________

2. How can you prove a linear equation is a straight line?
You can use a table to show the solutions of the equation, and then use the values in
your table to graph. Consider the equation: y = 2x + 1
What is y when x is 0, 1, 2…
In order to find the values of y, you have to substitute values of x
into the equation y = 2x + 1
x y = 2x + 1
0 ?
1 ?
2 ?
When x = 0, y = 2(0) + 1, so y = 1
When x = 1, y = 2(1) + 1, so y = 3
When x = 2, y = 2(2) + 1, so y = 5
These are the ordered pairs that are plotted on a graph; (0,1), (1,3),
(2,5)
When these points are plotted and connected, they make a straight
line.
x y
0 1
1 3
2 5
The graph below represents the equation: y = 2x + 1
Every point (ordered pair) on the line is a solution of the equation. Tell whether the following
points are a solution of the equation above and explain:
(1, 1) ________________________________________________________________________
(-1,1) ________________________________________________________________________