Linear Equations

1
Linear Equations
Linear equations are functions which have two
variables. They have an independent and
dependent variable.
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2
Independent and Dependent Variables
Independent variables are variables that you put
into the equations
Independent Variables
Dependent variables are variables that you solve
for
Dependent Variables
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
Dependent
Why?
Because it is the variable that is being solved
for
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