select the tables that show a proportional relationship

Explanation:

Step1: Recall proportional - relationship rule

For a proportional relationship between $x$ and $y$, $\frac{y}{x}=k$ (constant).

Step2: Check the first table

For the first table: $\frac{4}{12}=\frac{1}{3}$, $\frac{3}{9}=\frac{1}{3}$, $\frac{1}{3}=\frac{1}{3}$. The ratio $\frac{y}{x}$ is constant ($k = \frac{1}{3}$).

Step3: Check the second table

For the second table: $\frac{16}{4}=4$, $\frac{9}{3}=3$, $\frac{1}{1}=1$. The ratio $\frac{y}{x}$ is not constant.

Answer:

The first table shows a proportional relationship.