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In $y=mx$, is $m$, are there different implications of referring to $m$ as a "slope", a "coefficient", a "parameter"? Or perhaps the "slope coefficient" or "slope parameter"?

For context, I am describing a the process of parameterizing a linear model (as opposed to trying to interpret a description). As I understand, slope is a type of parameter, but it is not clear if there is a difference between parameter and coefficient.

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  • $\begingroup$ "Slope" is applicable since your model is a line (through the origin). "Parameter" and "coefficient" are more generic terms; either of those are fine for use in your context. $\endgroup$
    – J. M. ain't a mathematician
    Jan 4, 2012 at 15:38

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In $y=mx$, $m$ is slope, coefficient of $x$ and a paramter as well. There are no different implications if for example you call it a "slope parameter" or "slope coefficient" or simply "slope". These are just convenient terms to avoid confusion. Conceptual implications are not different.

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