Question

Select the tables that show a proportional relationship between x and y.


x 4 8 12
y 5 10 15

x 1 2 3
y 6 8 10

Answer 1

To determine if there is a proportional relationship between \( x \) and \( y \), we need to check if the ratios \( \frac{y}{x} \) are constant for the given pairs of values.

**Table 1:**
- \( x: 4, 8, 12 \)
- \( y: 5, 10, 15 \)

Calculating the ratios:
- For \( (4, 5) \): \( \frac{5}{4} = 1.25 \)
- For \( (8, 10) \): \( \frac{10}{8} = 1.25 \)
- For \( (12, 15) \): \( \frac{15}{12} = 1.25 \)

All ratios are \( 1.25 \). Thus, the first table shows a proportional relationship between \( x \) and \( y \).

**Table 2:**
- \( x: 1, 2, 3 \)
- \( y: 6, 8, 10 \)

Calculating the ratios:
- For \( (1, 6) \): \( \frac{6}{1} = 6 \)
- For \( (2, 8) \): \( \frac{8}{2} = 4 \)
- For \( (3, 10) \): \( \frac{10}{3} \approx 3.33 \)

The ratios are \( 6, 4, \) and \( 3.33 \), which are not constant. Therefore, the second table does not show a proportional relationship.

**Conclusion:**
- The first table shows a proportional relationship.
- The second table does not show a proportional relationship.