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If two values $m$ and $n$ are in direct variation, then

$m \propto n$

If the constant of proportionality is $q$ between them, then

$m = qn$

If $m$ and $n$ both are equal to zero or $m = 0$ and $n = 0$, then will they be called directly proportional to each other?

Samama Fahim
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1 Answers1

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Yes, but trivially so, in that the constant of proportionality can be any non-zero real number. That simply means than the direct proportionality of $m = n = 0$ is independent of the constant of proportionality $q$.

Typically, the sole restriction for two variables $m, n$ to be directly proportional is that the constant of proportionality, $q$ in your case, is non-zero.

See direct proportionality for more information.

amWhy
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  • But in this case $m = n$, then why should we say _ Proportional_? – Samama Fahim Apr 29 '13 at 20:19
  • Two variables that are equal are by default, proportional. For nonzero $m = n$, this just means that the constant of proportionality is $1$...Here is a situation where we can convey just as much information (and more) about the relationship between $m$ and $n$ by stating $m = n$ than by stating $m, n$ are "proportional" – amWhy Apr 29 '13 at 20:23
  • Thanks for the answer. Can I ask you for your email address? – Samama Fahim Apr 29 '13 at 20:27
  • I'd be happy to talk with you in a private chat sometime, when we both have the time...that's easy enough to set up...let me know some times that would be good for you... – amWhy Apr 29 '13 at 20:31
  • @amWhy: Nice write-up and exchange! +1 – Amzoti Apr 30 '13 at 00:40