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

Explanation:

Step1: Recall the condition for proportionality

For a proportional relationship (y = kx), where (k=\frac{y}{x}) (constant of proportionality).

Step2: Check the first table

• For (x = 1,y=\frac{5}{3}), (k_1=\frac{y}{x}=\frac{5}{3}\div1=\frac{5}{3}).
• For (x = 4,y=\frac{20}{3}), (k_2=\frac{y}{x}=\frac{20}{3}\div4=\frac{20}{3}\times\frac{1}{4}=\frac{5}{3}).
• For (x = 12,y = 20), (k_3=\frac{y}{x}=20\div12=\frac{5}{3}). Since (k_1 = k_2=k_3=\frac{5}{3}), the first table shows a proportional relationship.

Step3: Check the second table

• For (x = 9,y=\frac{5}{4}), (k_1=\frac{y}{x}=\frac{5}{4}\div9=\frac{5}{36}).
• For (x = 12,y = 2), (k_2=\frac{y}{x}=2\div12=\frac{1}{6}).
• For (x = 13,y=\frac{9}{4}), (k_3=\frac{y}{x}=\frac{9}{4}\div13=\frac{9}{52}). Since (k_1\neq k_2\neq k_3), the second table does not show a proportional relationship.

Answer:

The first table shows a proportional relationship.