There is absolutely no REQUIREMENT to do so. It is simply that many people prefer to work with whole numbers.
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Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
The answer will depend on the form of the equation. Whether it is an equation in one or more variables, whether it is linear or polynomial, there are different standard forms for exponential equations.
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Linear equations are a small minority of functions.
Most functions are not like linear equations.