Blog #4 Be the Professor

Professor Asma Aljarbou

Linear functions

Welcome to my lesson today for Linear Function, I hope you find it helpful for you, have good linear function understanding J

What is the linear function?

It is a function that has one input for every output and has constant rate of change.

Linear function formula   ---->  [ F(x)= mx + b ]

              Where:  m = slope (rise/run), b = Y-intercept, y and x are variables

What is one input for each output?

If we took the example of age and the person memory

·      Input: independent variable = age X

·      Output: dependent variables = the person memory F(x)

·     One input for each output: To have linear function we should have a unique value for every input X “not repeated value when it comes to independent values” and constant ROC.

Age X	The Person Memory F(x)
10	100%
20	95%
30	90%
40	85%

As you can see in the schedule we have one input for every output J !

Now let see if our function is a linear function!

To Calculate Average Rate of Change  ---->  [ ROC = Y2-Y1/X2-X1 ]

Let’s apply ROC to our variables and see if we have linear function!

ROC= 95-100/20-10 = -0.5

ROC= 90-95/30-20 = -0.5

ROC= 85-90/40-30 = -0.5

We have the same ROC so we have linear function J

* After evaluating ROC we can write the linear formula for the previous       example:  F (x) = -.5x + 105

Now let’s draw our Function:

To graph we need:

•       X-axis, which is the independent variables “age”
•       Y-axis, which I the dependent variables “memory”
•       Find our point ( x , y ) from our table = (10,100) (20,95) (30,90) (40,85)

*Cite may help you more to draw linear function graph:

          http://www.wikihow.com/Graph-Linear-Equations

          https://www.youtube.com/watch?v=hvn5x_ISago

Real life Example of linear function:

When a person sing a contract with At&T for 10 GB, they charge him $170 monthly. If he exceed the 10 GB they will charge him $15 for each GB he uses. So what is the relationship between the extra usage and total monthly cost?

 Total cost = $15(extra data he used) + 170 or y = 15x + 170

Feel free to contact me if you have any **Questions**

Thank you