(N/A) $(i)$ Boyle's Law: Robert Boyle $(1662)$ stated that at constant temperature,the volume of a fixed amount of any gas is inversely proportional to its pressure. $p \propto \frac{1}{V}$ (at constant $T$ and $n$). $\therefore pV = k_1$ (constant).
$(ii)$ Charles's Law: Jacques Charles showed that for a fixed mass of gas at constant pressure,the volume of the gas is directly proportional to its absolute temperature. $V \propto T$ (at constant $n$ and $p$). $\therefore \frac{V}{T} = k_2$ (constant).
$(iii)$ Gay-Lussac's Law: Joseph Gay-Lussac stated that at constant volume,the pressure of a fixed amount of a gas is directly proportional to its absolute temperature. $p \propto T$ (at constant $n$ and $V$). $\therefore \frac{p}{T} = k_3$ (constant).
$(iv)$ Avogadro's Law: Amedeo Avogadro $(1811)$ stated that equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules. $V \propto n$ (at constant $T$ and $p$). $\therefore V = k_4 n$.