Do the two tables show the same proportional relationship between x and​ y? Explain.

To determine whether the two tables show the same proportional relationship between \( x \) and \( y \), we need to calculate the ratio \( \frac{y}{x} \) for each pair in both tables and see if they remain constant.

For the first table:

| \( x \) | \( y \) | |---------|---------| | 50 | 1250 | | 75 | 1875 | | 100 | 2500 |

Calculating the ratios:

1. For the first pair: \[ \frac{y}{x} = \frac{1250}{50} = 25 \]
2. For the second pair: \[ \frac{y}{x} = \frac{1875}{75} = 25 \]
3. For the third pair: \[ \frac{y}{x} = \frac{2500}{100} = 25 \]

Each ratio \( \frac{y}{x} \) is equivalent to 25 in the first table.

For the second table:

| \( x \) | \( y \) | |---------|---------| | 3 | 4.2 | | 4 | 5.6 | | 5 | 7 |

Calculating the ratios:

1. For the first pair: \[ \frac{y}{x} = \frac{4.2}{3} \approx 1.4 \]
2. For the second pair: \[ \frac{y}{x} = \frac{5.6}{4} = 1.4 \]
3. For the third pair: \[ \frac{y}{x} = \frac{7}{5} = 1.4 \]

Each ratio \( \frac{y}{x} \) is equivalent to 1.4 in the second table.

Conclusion:

The two tables do not show the same proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to 25. In the second table, every ratio \( \frac{y}{x} \) is equivalent to 1.4.

Final answer:

No, each table shows a different proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to 25. In the second table, every ratio \( \frac{y}{x} \) is equivalent to 1.4.