Degree of dissociation. For the weak acid, $\alpha =\frac{{\Lambda }_m}{{\Lambda }_m^{\circ }}$.

Ostwald dilution law. $K_a=\frac{c{\alpha }^2}{1-\alpha }$, which rearranges to $K_a(1-\alpha )=c{\alpha }^2$. Substituting $\alpha ={\Lambda }_m/{\Lambda }_m^{\circ }$:

$$K_a\left(1-\frac{{\Lambda }_m}{{\Lambda }_m^{\circ }}\right)=c{\left(\frac{{\Lambda }_m}{{\Lambda }_m^{\circ }}\right)}^2.$$

Dividing both sides by ${\Lambda }_m$ and rearranging gives the standard linear form: $$\frac{1}{{\Lambda }_m}=\frac{c{\Lambda }_m}{K_a({\Lambda }_m^{\circ }{)}^2}+\frac{1}{{\Lambda }_m^{\circ }}.$$

Identify slope and intercept. Plotting $1/{\Lambda }_m$ (y-axis) against $c{\Lambda }_m$ (x-axis): $$S=\frac{1}{K_a({\Lambda }_m^{\circ }{)}^2},P=\frac{1}{{\Lambda }_m^{\circ }}.$$

Ratio. $\frac{P}{S}=\frac{1/{\Lambda }_m^{\circ }}{1/[K_a({\Lambda }_m^{\circ }{)}^2]}=K_a{\Lambda }_m^{\circ }$.

Answer: (A).