For the chemical equilibrium, ${\text{CaCO}}_{3(s)}\rightleftharpoons {\text{CaO}}_{(s)}+{\text{CO}}_{2(g)}$, $\Delta H_r^{\circ }$ can be determined from which one of the following plots?

For the reaction ${\text{CaCO}}_{3(s)}\rightleftharpoons {\text{CaO}}_{(s)}+{\text{CO}}_{2(g)}$, the equilibrium constant $K_p=P_{{\text{CO}}_2}$.According to the Van't Hoff equation (related to Arrhenius form):
$$\log K_p=\log A-\frac{\Delta H_r^{\circ }}{2.303RT}$$
Substituting $K_p=P_{{\text{CO}}_2}$:
$$\log P_{{\text{CO}}_2}=\left(-\frac{\Delta H_r^{\circ }}{2.303R}\right)\frac{1}{T}+\log A$$
This is a straight line equation of the form $y=mx+c$.A plot of $\log P_{{\text{CO}}_2}$ vs $1/T$ will be a straight line with slope $=-\frac{\Delta H_r^{\circ }}{2.303R}$. Since $\Delta H_r^{\circ }$ for this decomposition is positive, the slope will be negative.