## Define Linear Functions

A Function can be defined or explained as any event, action or task performed by any person for whom it is suited. Considering it under mathematical terms, a function is defined as the relation or association of any variable with the other in such a way that there exists a value or an output for each value of one variable defined.

For every input a particular output is defined. It can also be defined in terms of a set, in which for each of its element there exists a unique value. There are number of functions defined as complex functions, vector functions, real functions, scalar functions, **linear functions** and many other types of functions.

Now let us know about linear function. A linear function is defined as a function which satisfies the following given properties which are defined as is f (a*x) is equals to a* f(x) and second property is defined as f (x + y) is equals to f (x) + f (y) where ‘x’ and ‘y’ are used as variables for the functions and ‘a’ is a constant term that is multiplied with the function.

Function can be easily determined when the coordinates for any line are known. For example: If a coordinate is given as (4, 6) where 4 is said to be x coordinate and similarly 6 is y coordinate. Then, the function for this coordinate will be written as f(4) is equals to 6. Similarly if we know the function then the coordinates can be easily determined. Suppose, f(2) is given to be 10. Then the coordinate for this function will be determined as (2, 10) as the coordinates of linear function.

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