select the tables that show a proportional relationship between x and y.

Explanation:

Step1: Recall proportional - relationship rule

For a proportional relationship between $x$ and $y$, the ratio $\frac{y}{x}$ must be constant.

Step2: Check first table

For the first table: When $x = 4,y = 1$, $\frac{y}{x}=\frac{1}{4}$; when $x = 5,y = 2$, $\frac{y}{x}=\frac{2}{5}$; when $x = 8,y = 5$, $\frac{y}{x}=\frac{5}{8}$. Since $\frac{1}{4}\neq\frac{2}{5}\neq\frac{5}{8}$, it is not a proportional relationship.

Step3: Check second table

When $x = 4,y = 1$, $\frac{y}{x}=\frac{1}{4}$; when $x = 8,y = 2$, $\frac{y}{x}=\frac{2}{8}=\frac{1}{4}$; when $x = 12,y = 3$, $\frac{y}{x}=\frac{3}{12}=\frac{1}{4}$. Since the ratio $\frac{y}{x}$ is constant ($\frac{1}{4}$), it is a proportional relationship.

Answer:

The second table shows a proportional relationship between $x$ and $y$.