Explain Boyle's law,derive its mathematical equation,and describe the isothermal graph.

(N/A) Boyle's law states that at a constant temperature $(T)$,the pressure $(P)$ of a fixed amount (number of moles $n$) of gas varies inversely with its volume $(V)$.
Mathematical derivation:
$P \propto \frac{1}{V}$ (at constant $T$ and $n$)
$P = k \cdot \frac{1}{V}$
$PV = k$ (where $k$ is a constant)
For two different states of the gas: $P_1V_1 = P_2V_2$.
Isothermal graph: $A$ plot of $P$ versus $V$ at constant temperature is called an isotherm and it is a rectangular hyperbola. The graph shows that as temperature increases,the curve shifts further from the origin.