linear equations linear equations are functions which have two variables. they have an independent...
TRANSCRIPT
Linear Equations
Linear equations are functions which have two variables. They have an independent and dependent variable.
Independent and Dependent Variables
Independent VariablesIndependent variables are variables that you put into the equations
Dependent VariablesDependent variables are variables that you solve for
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
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
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
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 )
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
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
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
Class Examples:
2a + b = 4
3r - 2s = 7
2 + x = y
This powerpoint was kindly donated to www.worldofteaching.com
http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.