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 \(x = 2,y=5\), the ratio \(\frac{y}{x}=\frac{5}{2}=2.5\)
When \(x = 4,y = 10\), the ratio \(\frac{y}{x}=\frac{10}{4}=2.5\)
When \(x=6,y = 15\), the ratio \(\frac{y}{x}=\frac{15}{6}=2.5\)
Since the ratio \(\frac{y}{x}\) is constant (\(k = 2.5\)), the first table shows a proportional relationship.

Step2: Calculate the ratio for the second table

For the second table:
When \(x = 1,y=2\), the ratio \(\frac{y}{x}=\frac{2}{1}=2\)
When \(x = 2,y = 5\), the ratio \(\frac{y}{x}=\frac{5}{2}=2.5\)
When \(x=4,y = 17\), the ratio \(\frac{y}{x}=\frac{17}{4}=4.25\)
Since the ratio \(\frac{y}{x}\) is not constant, the second table does not show a proportional relationship.

Answer:

Only the first table shows a proportional relationship.