Question

select the tables that show a proportional relationship between x and y.
work it out
not feeling ready yet? these can help:
find the constant of proportionality from a table
lesson: proportional relationships

Explanation:

Step1: Calculate ratios for the first table

For the first table:

• When \(x = 9,y = 2\), the ratio \(\frac{y}{x}=\frac{2}{9}\)
• When \(x = 12,y = 3\), the ratio \(\frac{y}{x}=\frac{3}{12}=\frac{1}{4}\)
• Since \(\frac{2}{9}

eq\frac{1}{4}\), the first table does not show a proportional relationship.

Step2: Calculate ratios for the second table

For the second table:

• When \(x = 1,y = 4\), the ratio \(\frac{y}{x}=\frac{4}{1} = 4\)
• When \(x = 2,y = 8\), the ratio \(\frac{y}{x}=\frac{8}{2}=4\)
• When \(x = 3,y = 12\), the ratio \(\frac{y}{x}=\frac{12}{3}=4\)
• Since the ratio \(\frac{y}{x}\) is constant (\(k = 4\)), the second table shows a proportional relationship.

Answer:

The second table shows a proportional relationship.