Linear equations are functions which have two variables. They have an independent and dependent variable.

1. Linear Equations
Linear equations are functions which
have two variables. They have an
independent and dependent variable.

2. Independent and Dependent
Variables
Independent Variables
Independent variables
are variables that you
put into the equations
Dependent Variables
Dependent variables
are variables that you
solve for

3. Just as common sense would dictate. If
something is independent, then it is on its
own. But if it is dependent, then it relies on
someone or something else.
A dependent variable relies on what is used in
place of the independent variable

4. y = 2x - 4
Using the equation above, y has to be the
variable
Why? Because it is the variable that is
being solved for
Dependent

5. Because linear equations have two
variables,there are many possible
combinations of answers
Those possible solutions are written as
ordered pairs. Usually an ordered pair
is written with the independent variable
first then the dependent variable

6. Example: y = 3x - 5
Because we solved for y, then x is
the independent variable
The ordered pair would then be
written as ( x , y )

7. If we do not know which variable is
independent, then we choose one. No
matter which one is independent, we will
still produce similar ordered pairs
( r , s ) is similar to ( s , r )
Not congruent/equal

8. Most of the time when we use the
variables x & y in an equation, x is
independent and y is dependent
There are some exceptions, but we will
work with those at a much later time

9. As said before, there are many possible
ordered pairs
To find more than one solution, we use a
Table of Values
x y
2 3
-2 1
0 -3

10. Class Examples:
2a + b = 4
3r - 2s = 7
2 + x = y

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