The law that explains the relationship between the pressure and volume of a gas is known as Boyle's Law. This gas law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. In mathematical terms, this can be expressed as P1V1 = P2V2, where P represents pressure and V represents volume. Boyle's Law is fundamental in understanding gas behavior and is applicable in various scientific fields, including physics, chemistry, and engineering, particularly in scenarios involving ideal gases.