The ideal gas equation is pV = nRT
From that you can derive several equations, depending on which variables are fixed.
1) When n and T are fixed:
pV = nRT = constant
pV = constant => p1 V1 = p2 V2 => p1 / V2 = p2 / V1 ---> Boyle's Law
2) When n and V are constant:
p / T = nR/V = constant
p / T = constant => p1 / T1 = p2 / T2 ----> Gay - Lussac's Law
3) when n and p are constant
V / T = nR/p = constant
V / T = constant => V1 / T1 = V2 / T2 ---> Charles' Law
4) When only n is constant
pV / T = nR = constant
pV / T = constant => p1 V1 / T1 = p2 V2 / T2 ----> Combined gas law.
There you have the four equations that agree with the ideal gas law.
