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

Explanation:

Step1: Calculate the ratio for the first table

For the first table:

• When (x = 7), (y = 5), ratio (\frac{y}{x}=\frac{5}{7}\approx0.71)
• When (x = 8), (y = 6), ratio (\frac{y}{x}=\frac{6}{8}=\frac{3}{4} = 0.75)
• When (x = 12), (y = 10), ratio (\frac{y}{x}=\frac{10}{12}=\frac{5}{6}\approx0.83) Since the ratios are not equal, this table does not show a proportional relationship.

Step2: Calculate the ratio for the second table

For the second table:

• When (x = 4), (y = 3), ratio (\frac{y}{x}=\frac{3}{4}= 0.75)
• When (x = 8), (y = 6), ratio (\frac{y}{x}=\frac{6}{8}=\frac{3}{4}= 0.75)
• When (x = 12), (y = 9), ratio (\frac{y}{x}=\frac{9}{12}=\frac{3}{4}= 0.75) Since the ratios are equal ((\frac{y}{x}=\frac{3}{4})), this table shows a proportional relationship.

Answer:

Only the second table shows a proportional relationship.