Boyle's Law States: PV=k where P is pressure, V is volume, and k is a constant (the number must stay the same). If the pressure inside the sauce packet goes up, what must happen to the volume of air inside the packet to maintain the same value of constant "k"?

In other words, this law says: on the same temperature (important, there is no temperature change), if you decrease the volume of a gas (for example by squeezing it), the pressure inside the gas will increase. It's also true the other way around. In order to decrease the pressure of the gas, you need to increase the volume (for example, by stretching it out).

So if the pressure goes up, the volume has decreased.