Linear Equations Linear equations are functions which have two variables. They have an independent...
-
Upload
maurice-cannon -
Category
Documents
-
view
217 -
download
3
Transcript of Linear Equations Linear equations are functions which have two variables. They have an independent...
![Page 1: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/1.jpg)
Linear Equations
Linear equations are functions which have two variables. They have an independent and dependent variable.
![Page 2: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/2.jpg)
Independent and Dependent Variables
Independent VariablesIndependent variables are variables that you put into the equations
Dependent VariablesDependent variables are variables that you solve for
![Page 3: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/3.jpg)
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
![Page 4: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/4.jpg)
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
![Page 5: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/5.jpg)
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
![Page 6: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/6.jpg)
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 )
![Page 7: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/7.jpg)
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
![Page 8: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/8.jpg)
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
![Page 9: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/9.jpg)
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
![Page 10: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/10.jpg)
Class Examples:
2a + b = 4
3r - 2s = 7
2 + x = y
![Page 11: Linear Equations Linear equations are functions which have two variables. They have an independent and dependent variable.](https://reader036.fdocuments.in/reader036/viewer/2022082817/56649dde5503460f94ad6750/html5/thumbnails/11.jpg)
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.