Identify the table that demonstrates a proportional relationship.(1 point)

Question

Responses

x y
10 2
15 3
40 8


x y 10 2 15 3 40 8

x y
8 2
12 3
40 4
x y 8 2 12 3 40 4

x y
2 10
5 20
6 30
x y 2 10 5 20 6 30

x y
4 2
9 3
16 4

Answer 1

To identify a proportional relationship, we need to see if the ratio \( \frac{y}{x} \) is constant across all pairs of values in a given set.

Let's check each table:

1. First table:

   • \( \frac{2}{10} = 0.2 \)
   • \( \frac{3}{15} = 0.2 \)
   • \( \frac{8}{40} = 0.2 \)
   • All ratios are equal (0.2), so this table does demonstrate a proportional relationship.

2. Second table:

   • \( \frac{2}{8} = 0.25 \)
   • \( \frac{3}{12} = 0.25 \)
   • \( \frac{4}{40} = 0.1 \)
   • The ratios are not all equal, so this table does not demonstrate a proportional relationship.

3. Third table:

   • \( \frac{10}{2} = 5 \)
   • \( \frac{20}{5} = 4 \)
   • \( \frac{30}{6} = 5 \)
   • The ratios are not all equal, so this table does not demonstrate a proportional relationship.

4. Fourth table:

   • \( \frac{2}{4} = 0.5 \)
   • \( \frac{3}{9} \approx 0.333 \)
   • \( \frac{4}{16} = 0.25 \)
   • The ratios are not all equal, so this table does not demonstrate a proportional relationship.

Based on this analysis, only the first table demonstrates a proportional relationship.