Question

How do you turn a proportionality between variables into an equation?

Answer 1

Answer. By adding the proportionality constant .

Explanation:

suppose 'x' a  is directly proportional to the 'y' , where x and y are variables:

x ∝ y

with an input of constant value 'K' proportionality relation gets converted into  an equation:

x = K y

For example : Gravitational force is directly proportional to the product of two masses and inversely proportional to the square of the distance between the two masses.

F ∝ $\frac {m_1m_2}{r^{2}}$

To convert this proportionality relation constant 'G'  was introduced known as gravitational constant whose value remains constant under every conditions.

$F=\frac {G\times m_1m_2}{r^{2}}$

$G=6.67408\times 10^{-11}m^3Kg^{-1}s^{-2}$