A linear function when graphed takes the form of a straight line.
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A linear function is a function, or equation, that when graphed, will form a straight line.
There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.
I suppose it is written in invisible form!
If it can be written in the form y = mx + c where m and c are constants [or, equivalently, ax + by = k where a, b and k are constants] then y is a linear function of x.
Your age is a linear function (of time).