To solve this problem, we need to understand Boyle's Law.$\\$Boyle's Law states that for a given mass of gas at constant temperature,$\\$the pressure $(P)$ of the gas is inversely proportional to its volume $(V). \\$Mathematically, this is expressed as:$\\ PV =$constant$\\$This implies that if we plot $P$ against $\frac{1}{V},$ we should get a straight line.$\\$Let's analyze the options:$\\$Option 1:$\\$The graph shows $P$ versus $V$ with curves for different temperatures.$\\$This is not a linear relationship, so it doesn't represent Boyle's Law.$\\$Option 2:$\\$The graph shows $P$ versus $\frac{1}{V}$ with straight lines for different temperatures.$\\$This is consistent with Boyle's Law, as $P \propto \frac{1}{V}. \\$Option 3:$\\$The graph shows $P$ versus $\frac{1}{V}$ with curves, not straight lines.$\\$This does not represent Boyle's Law.$\\$Option 4:$\\$The graph shows $P$ versus $T$ with straight lines for different volumes.$\\$This is not related to Boyle's Law, as it involves temperature.$\\$Therefore, the correct graphical representation of Boyle's Law is Option 2.