# Would it be valid to say $y \propto 2x$ instead of $y \propto x$?

Would it be acceptable to write $$y \propto 2x$$ or would it be wrong to add the $$2$$? I just want to describe a relationship in more detail.

• Voting to reopen. This is a perfectly clear question with a good answer below. Commented May 20 at 11:59
• @gandalf61 I agree. I have tidied up the question. Commented May 20 at 12:49
• If what you mean is $y=2x$, then write that. If what you mean is that $y$ is proportional to $x$, then it is also proportional to $2x$, $3x$, $17.9x$, $\pi x$, etc. so why would you pick $2x$? Commented May 20 at 22:53

I don't think it would be wrong, but perhaps unusual and it doesn't really describe the relationship in more detail. $$y\propto x$$ simply means $$y=cx$$ where $$c$$ doesn't depend on $$x$$. For all you know, $$c$$ could be a million or $$10^{-20}$$ but those factors aren't really relevant for the relationship between $$y$$ and $$x$$ – that simply is that $$y$$ increases linearly with $$x$$. So usually, all constant factors are absorbed into the proportionality symbol.
• You "could" of course say that. However, I don't see why you would say that. If you already know, that $y$ depends linearly on $x$ and that the slope is $2$, why then not simply write $y = 2x$? Perhaps if you add some context, one could better understand why you want to use the $\propto$ symbol and if it makes sense. Commented May 20 at 10:04
• It sure sounds like something physicists would write. Actually, if $c$ has dimensions, for any dimensional quantities writing $x\propto cy$ would be the only way for the statement to make sense. But of course, mathematicians do not concern themselves with these things too much Commented May 20 at 14:31
$$y \propto 2x$$ doesn't convey any more information than $$y \propto x$$. Therefore, while not technically incorrect, the inclusion of the $$2$$ is unnecessary. It doesn't add anything more.