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Tuesday, December 2, 2014

Blog Post # 4

Linear Functions
Purpose: To show the class how to find and graph linear functions.
Linear function - a function where the rate of change is constant at every interval and the graph results in a straight line.
The equation of a linear line is y=mx+b where m is the rate of change, x is the x-value, and b is the y-intercept.

You can tell that this function is linear since the rate of change is the same across every point of the graph. 

http://image.tutorvista.com/content/feed/u1053/line%20graph.PNG
Linear Function (y=x)
"Line Graph." Free Math Tutoring. Web. 3 Dec. 2014. <http://math.tutorvista.com/statistics/line-graphs.html>. 
Ex:
Rate of change (ROC) = Y2-Y1 
                                         X2-X1

 2-1/2-1 = 1/1 = 1
 3-2/3-2 = 1/1 = 1 
 4-3/4-3 = 1/1 = 1
 ............................ 
     Slope or ROC is also defined as   Rise (ΔY)
                                                          Run (ΔX)
Ex: 1/1 = 1
       1/1 = 1
       1/1 = 1
       1/1 = 1
       ...........
The rate of change is the same at every interval which means that the function shown above is linear.  
Non-linear Function (y=|x|)
"Advanced Tutorial - Gradients, Linearity, and Sparsity." Solver. Web. 3 Dec. 2014. <http://www.solver.com/advanced-tutorial>. 

 
This function is not linear since it does not form a straight line and he rate of change varies throughout the function.

Ex: (5-10)/(-5+10) = (-5/5) = 1
       (10-5)/(10-5) = (5/5) = 1  

     
Linear Table
Table of Linear Function
  "Function Tables." Online Math Help. Web. 3 Dec. 2014. <http://www.mathcaptain.com/algebra/function-tables.html>.


You can also find a linear function using data tables.

If the X and Y values are changing at a constant rate then the function that the data represents is linear.
  
How to write a table or graph as a linear equation in slope-intercept form.  
  • Find the slope Y2-Y1 
                              X2-X1          

    (3-1)/(0--1) = 2/1 = 2
  • Set up the equation: (y=2x+b)
  • Take one of the coordinate pairs and substitute the x and y values into the equation: (1 = 2(-1) + b)
  • Multiply 2 by -1: (1 = -2 + b)
  • Add 2 to both sides: (3 = b)
  • Substitute the value of b into the equation: (y = 2x + 3)
  • To check the equation, substitute another coordinate point into the equation and see if the equation works. : (5 = 2(1) + 3) = (5 = 2 + 3) = (5 = 5).
How to rewrite an equation in slope intercept form5x + 2y + 7 = 0
  • Subtract 7 from both sides: (5x + 2y = -7)
  • Subtract 5x from both sides: (2y = -5x - 7)
  • Divide both sides by 2: (y = (-5x - 7)/2)
  • Equation in slope intercept formy = (-5x - 7)/2
 

3 comments:

  1. Nice job Jeffrey! I personally really liked your step by step bullet point set up at the end of the lesson. It made things clear, easy and simple!

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  2. I really liked that you gave many examples on different ways you can learn it!

    ReplyDelete
  3. jeffrey,

    i really like your second example and how you worked step by step through it to ensure understanding! all of your examples are good and the lesson is solid. maybe you could have added a little more explanation of what rate of change is, but other than that, nice job!

    professor little

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