You can basically use any letter for a constant. "c" is often used because it's the first letter of "constant"; the use of "k" probably arises either from the fact that it has the same sound, in English, as "k"; or from other languages where the word "constant" is written with a "k" (e.g., "Konstante" in German).
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Any letter of the alphabet can be used, but c and k are often used - possibly because of the phonetic start of the word "constant".
Various options: y is directly proportional to k, with x as the constant of proportionality; y is directly proportional to x, with k as the constant of proportionality; x is inversely proportional to k, with y as the constant of proportionality; x is directly proportional to y, with 1/k as the constant of proportionality; k is directly proportional to y, with 1/x as the constant of proportionality; and k is inversely proportional to x, with y as the constant of proportionality.
It is the constant of proportionality.
When there is a direct proportionality y = kx y = 75 k = 15 → 75 = 15x → x = 75/15 = 5
Yes, it does. Every time there are variables in direct or inverse relationship, there is a constant of proportionality.
Y=k/x where k is the constant of proportionality is an example of indirect or inverse variation. They are the same thing.