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What similarities and differences are there between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function?

  • Algebra -

    A function is a rule that explains how one variable can be computed from one or more other variables. A linear equation of the form y = mx + b is a function.

    If you have an equation without ONLY one variable on one side, it is technically not a function, in my opinion.

    b = mx - y and m = y/x are not explicit functions as written, if m and b are constants, but can be rewritten as linear functions. Those might be called implicit functions.

    I think one get lost in semantics with questions like this. I wonder whether it really helps in teaching math.

  • Algebra -

    With a function, for every X there is only one Y. With linear equations, for every X, there can be more than one Y.

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