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Definition of Linear Function. A function that can be graphically represented in the Cartesian coordinate plane by a straight line is called a Linear Function.
$$f(ax) = af(x)$$. where $x$ and $y$ are vectors and $a$ is a scalar. Roughly, this means that inputs are proportional to outputs and that the function is additive. We get the name 'linear' from the prototypical example of a linear function in one dimension: a straight line through the origin.