What is this formula called: #P_1V_1 = P_2V_2#?

#"Boyle's Law"# or the #"Boyle Mariotte Law"# is an experimental gas law that describes that behaviour of relationship of pressure to volume in a closed system.

For a given quantity of gas at a given temperature, #PV=k#, and thus #P_1V_1=P_2V_2#.

Boyle's law states that for a fixed mass of an ideal gas, held at a constant temperature, the volume of the gas is inversely related to the pressure applied to it.

Mathematically: #P_1V_1=P_2V_2#

Which tell us that if #P_1toP_2# then #V_1toV_2#

To sort out this inverse relationship we can use an example with the units Bole used. Pressure was measured in inches of mercury: #i#.
Volume was measured in cubic centimeters: #c#.

Let: #P_1=2i and V_1=5c# and we will increase the pressure to #4i#

#P_1V_1=P_2V_2#

#2i*5c=4i*V_2#

#(cancel(2i)1*5c)/(cancel(4i)2)=V_2#

#1/2*5c=V_2#

By doubling the pressure we have cut the volume of the gas by one half. Using the same formula you can calculate the opposite effect of cutting the pressure in half to double the volume.

It may be more clear if you write the formula in another way:

#P_1V_1=P_2V_2to#

#V_2=(P_1V_1)/P_2#

This shows as the pressure #darr# from #P_1 to P_2# the volume #V_2 uarr#.

As the pressure #uarr# from #P_1 to P_2# the volume #V_2 darr#.

There are images here: https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/gases-5/gas-laws-51/boyle-s-law-volume-and-pressure-254-8360/