At constant temperature, pressure is inversely proportional to volume: P ∝ 1/V. Drag the piston left to decrease volume — watch particles collide with walls more frequently, increasing pressure.
At constant pressure and amount of gas, volume is directly proportional to absolute temperature: V ∝ T. Increase the temperature — particles speed up, pushing the piston outward to maintain constant pressure.
The total pressure of a gas mixture equals the sum of the partial pressures: P_total = P₁ + P₂ + P₃ + .... Add different gases and observe how each contributes to total pressure independently.