Question

Select the tables that show a proportional relationship between x and y.
x y x y
8 1 6 2
10 2 9 3
14 4 12 4

Answer 1

To determine whether there is a proportional relationship between \( x \) and \( y \) in each pair of tables, we need to check if the ratio \( \frac{y}{x} \) remains constant.

Let's check each pair of values:

1. For the first table:
- \( (8, 1) \): \( \frac{y}{x} = \frac{1}{8} \)
- \( (10, 2) \): \( \frac{y}{x} = \frac{2}{10} = \frac{1}{5} \)
- \( (14, 4) \): \( \frac{y}{x} = \frac{4}{14} = \frac{2}{7} \)

The ratios are not equal, so there is no proportional relationship.

2. For the second table:
- \( (6, 2) \): \( \frac{y}{x} = \frac{2}{6} = \frac{1}{3} \)
- \( (9, 3) \): \( \frac{y}{x} = \frac{3}{9} = \frac{1}{3} \)
- \( (12, 4) \): \( \frac{y}{x} = \frac{4}{12} = \frac{1}{3} \)

All ratios are equal to \( \frac{1}{3} \), so there is a proportional relationship.

In summary:

- The first table does not show a proportional relationship.
- The second table does show a proportional relationship.