Question

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 \(x = 4,y = 6\), the ratio \(\frac{y}{x}=\frac{6}{4}=\frac{3}{2}\)
When \(x = 8,y = 9\), the ratio \(\frac{y}{x}=\frac{9}{8}\)
Since \(\frac{3}{2}
eq\frac{9}{8}\), the first table does not show a proportional relationship.

Step2: Calculate the ratio for the second table

For the second table:
When \(x = 0,y = 0\), the ratio is undefined (but \(y = kx\) holds as \(0=k\times0\) for any \(k\))
When \(x = 7,y = 7\), the ratio \(\frac{y}{x}=\frac{7}{7} = 1\)
When \(x = 10,y = 10\), the ratio \(\frac{y}{x}=\frac{10}{10}=1\)
Since the ratio \(\frac{y}{x}=1\) (constant \(k = 1\)), the second table shows a proportional relationship.

Answer:

The second table shows a proportional relationship.