"what information does the slope of the line give you when graphing the pressure versus 1/volume at constant temperature for 1 mole of gas? "

Hello!

The slope of the line given by graphing pressure vs 1/Volume at constant temp for one mole of gas will give you the value for nRT from equation PV=nRT

So set nRT=slope and take the constant number mole of gas and the constant temp and solve for R the universal gas constant. You arm for pressure and litters for volume to get R in units of L*atm/mol*k

Hope this helps you! Thanks!!

Uncle grandma