Why is k constant in Boyle’s law?

was first formulated as an experimental gas law which described how the pressure of a gas decreased when the volume of said gas increased.
A more formal description of states that the pressure exerted by a mass of ideal gas is inversely proportional to the volume it occupies if temperature and amount of gas remain unchanged.
Mathematically this can be written as
##P## ##alpha 1/V## or ##PV = constant##
This is where a ##k## is usually seen as it is often used to describe a constant value. So the ##k## you are referring to is
##PV = constant = k##
This can be easily derived from the ##PV = nRT## for the conditions specified by Boyle’s law.
We need to keep the amount of gas which represents the number of and the temperature constant. Since ##R## is a constant already the becomes
##PV = nRT = k##
Therefore ##k## must be constant in order to allow for a relationship to be set between pressure and volume.