Given the following table of values for variables $x$ and $y$: (1, 2), (2, 4), (3, 6), (4, 8), does the table show a proportional relationship between $x$ and $y$?

• A. No, because the values of $y$ do not increase by the same amount as $x$.
• B. Yes, because the sum $x+y$ is constant.
• C. No, because the difference $y-x$ is not constant.
• D. Yes, because the ratio $\frac{y}{x}$ is constant for all pairs.

Answer: (D)

Verified step by step guidance

1. Understand that a proportional relationship between two variables x and y means that y is directly proportional to x. This implies that the ratio \( \frac{y}{x} \) should be constant for all pairs of values.
2. Calculate the ratio \( \frac{y}{x} \) for each pair given in the table: (1, 2), (2, 4), (3, 6), and (4, 8).
3. For each pair, divide the y-value by the corresponding x-value, i.e., compute \( \frac{2}{1} \), \( \frac{4}{2} \), \( \frac{6}{3} \), and \( \frac{8}{4} \).
4. Compare these ratios to check if they are all equal. If they are equal, it confirms that y is proportional to x.
5. Conclude that since the ratio \( \frac{y}{x} \) is constant for all pairs, the table shows a proportional relationship between x and y.