1. For a low-density gas at constant volume, the ideal gas law gives $P \propto T$ where $T$ is the absolute temperature in kelvin.

2. If pressure is plotted against temperature in $^{\circ}\mathrm{C}$, the graph is a straight line: $P \propto (t + 273)$ where $t$ is temperature in $^{\circ}\mathrm{C}$.

3. Therefore, for any gas at constant volume, the pressure becomes zero when $t + 273 = 0$ $t = -273^{\circ}\mathrm{C}$

4. In the given graph, point $K$ is the common temperature where the straight-line $P$ vs $t$ graphs extrapolate to zero pressure.

5. Hence, the temperature corresponding to point $K$ is $-273^{\circ}\mathrm{C}$

6. Checking options:

   • A: $-273^{\circ}\mathrm{C}$ ✅
   • B: $-373^{\circ}\mathrm{C}$ ❌
   • C: $-100^{\circ}\mathrm{C}$ ❌
   • D: $-40^{\circ}\mathrm{C}$ ❌

So the correct option is A.