Neither variable appears anywhere in the equation in a denominator,
or raised to any power except the first power.
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Your age is a linear function (of time).
Yes, y=-5x+3 is a linear function. We know that by two factors. First, if you plot the function, you find that it draws a straight line, hence the term linear. Second, if you inspect the non-constant terms, you find that all of the are in the first power, i.e. there are no "squareds", "cubes", square roots", etc. This also makes it s linear function.
A linear function is a function, or equation, that when graphed, will form a straight line.
A linear objective function and linear constraints.
A linear function when graphed takes the form of a straight line.