Explain the law relating pressure and temperature.

(N/A) Pressure in well-inflated tires of automobiles is almost constant,but on a hot summer day,a tire may burst if the pressure is not adjusted properly. During winters on a cold morning,one may find the pressure in the tires of a vehicle decreased considerably.
Law: At constant volume,the pressure of a fixed amount of a gas varies directly with its absolute temperature.
Mathematically:
$p \propto T$ (at constant $V$) .... (Eq.-$i$)
$p = K_3 T$ (at constant $V$) .... (Eq.-$ii$)
So,$\frac{p}{T} = K_3 =$ constant .... (Eq.-$iii$)
Law Statement: "At constant volume,the ratio of pressure and absolute temperature of a gas is constant."
Formula for changes in temperature and pressure at constant volume: Suppose,at constant volume,the initial pressure is $p_1$ and initial temperature is $T_1$,and the final pressure is $p_2$ and final temperature is $T_2$.
According to Gay-Lussac's Law:
$\frac{p_1}{T_1} = k_3 = \frac{p_2}{T_2}$
Thus:
$\frac{p_1}{T_1} = \frac{p_2}{T_2}$ .... (Eq.-$iv$)
$\frac{p_1}{p_2} = \frac{T_1}{T_2}$ .... (Eq.-$v$)
$p_1 T_2 = p_2 T_1$ .... (Eq.-$vi$)
Isochore Graph: The pressure $vs$ temperature (Kelvin) graph at constant molar volume is shown in the figure.