Probably because it is the first letter of the Cartesian plane.
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C=100
y = cx where c is the constant of proportionality.
The letters b and c could represent almost any number. They are used in equations normally because they are unknown, and so that we can figure out their values through solving the problem.
None. The speed of light is usually assumed to be constant. The symbol used to represent the speed of light is "C", as in E=MC2. Then why is it called a variable speed?
Any letter in the alphabet can be used to represent a variable in algebra.