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

Explanation:

Step1: Calculate the ratio for the first table

For the first table:

• When (x = 4,y = 3), the ratio (\frac{y}{x}=\frac{3}{4}=0.75)
• When (x = 6,y = 8), the ratio (\frac{y}{x}=\frac{8}{6}=\frac{4}{3}\approx1.33)
• Since (0.75\neq1.33), the first table does not show a proportional relationship.

Step2: Calculate the ratio for the second table

For the second table:

• When (x = 3,y = 4), the ratio (\frac{y}{x}=\frac{4}{3})
• When (x = 6,y = 8), the ratio (\frac{y}{x}=\frac{8}{6}=\frac{4}{3})
• When (x = 15,y = 20), the ratio (\frac{y}{x}=\frac{20}{15}=\frac{4}{3})
• Since the ratio (\frac{y}{x}) is constant ((\frac{4}{3})), the second table shows a proportional relationship.

Answer:

Only the second table shows a proportional relationship.