#S  
y(x) =  Σ  [S_{n}*x + B_{n}] + S_{0}*x + B_{0} 
n=1 
This is my formula designed to turn any set of coordinates into a single absolute value equation that will intercept, and draw a line between, each and every single point. This algorithim eliminates computationaly costly branching when computers use formulas generated by this algorithim.
I used javascript to program the following demo which will take any set of any number of coordinates and spit out an absolute value equation that will intercept all the points. Go ahead, type in some coordinates. It won't bite. Also, very important, you can enter in as many coordinates or as few coordinates as you want. This formula can accept 2 coordinates just as well as 2,000 coordinates. To enter in a new coordinate, simply end the line with a comma, put in a starting opening parenthese, put in your x value, put in a comma, put in your y value, and end it with a closing parenthese.
Example #1: 3 coordinates You can also edit theese boxes to any number of any coordinates you want.  Example #2: 2 coordinates You can also edit theese boxes to any number of any coordinates you want.  Example #3: 15 coordinates You can also edit theese boxes to any number of any coordinates you want. 

Resulting Equation  Resulting Equation  Resulting Equation 
 
Try It Out! Entering in a value for x into the following equation will generate the corresponding number.  Try It Out! Entering in a value for x into the following equation will generate the corresponding number.  Try It Out! Entering in a value for x into the following equation will generate the corresponding number. 
y() =  y() =  y() = 
Equation Graph The following chart visually displays what the graph looks like. Special thanks to XY.js  Equation Graph The following chart visually displays what the graph looks like. Special thanks to XY.js  Equation Graph The following chart visually displays what the graph looks like. Special thanks to XY.js 
The following steps are the same ones used in the demo above which are used to generate the absolute value equation. The example section will demonstrate how you do the steps to help you understand the equation.
Steps  Mathematical Represenation  Example  

 N/A  (x, y) = {(1, 0), (4, 1), (2, 3)}  
 N/A  (x, y) = {(1, 0), (2, 3), (4, 1)}  
1 from the pairs and store them in list B.  B_{n} = X_{n+1} for  B = {2}  
 M_{n} =
 M = {1, 2}  
 S_{n} =
 S = {1.5}  
 S_{0} = M_{1} + ΣS = M_{#M}  ΣS  S_{0} = 0.5  

 B_{0} = 4  

 y(x) = 1.5*x  2*x + + .5*x  4 
I hope you learned something new on this page reguarding piecewise calculus. And, I hope you will use it for good in this world. I know I will.