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They are the same.
Only if the two functions really represent the same function.
Linear programming approach does not apply the same way in different applications. In some advanced applications, the equations used for linear programming are quite complex.
Functions and linear equations are the same in that they both deal with x and y coordinates and points on a graph but have differences in limitations, appearance and purpose. Often, functions give you the value of either x or y, but linear equations ask to solve for both x and y.
A linear encoder is a instrument that uses precise measurements. A linear encoder is used on many different types of objects, but is used for the same purpose of measuring positions.