Constant of proportionality basically comes from mathematics.
In Physics and other branches of Science or Subjects it is applied and used to describe variables.
If change in one variable is always accompanied by a change in another variable, and if the changes between the two are always related by a constant multiplier, two variables are termed as proportional to each other. And the constant multiplier is called the constant of proportionality.
Example: In this particular example both direct as well inverse proportion is in one equation.
Law of Universal Gravitation states that the force of attraction ##F## between two bodies is directly proportional to the product of masses of the two bodies. It is also inversely proportional to the square of the distance between the two bodies.
##F prop M_1.M_2##
Also ##F prop 1/r^2##
Combining the two we obtain the proportionality expression
##F prop (M_1.M_2)/r^2##
##F =G (M_1.M_2)/r^2##
Where ##G## is constant of proportionality.
It has the value ##6.67408 xx 10^-11 m^3 kg^-1 s^-2## and also called Universal Gravitational Constant.
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