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

Question

Responses

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
x y 4 2 9 3 16 4

x y
10 2
15 3
40 8


x y 10 2 15 3 40 8

Answer 1

A proportional relationship is characterized by a constant ratio between the variables \( x \) and \( y \). To determine which table demonstrates this, we need to calculate the ratio of \( y \) to \( x \) for each pair in all four options.

1. For the first table:

   • \( \frac{2}{8} = 0.25 \)
   • \( \frac{3}{12} = 0.25 \)
   • \( \frac{4}{40} = 0.1 \)
   • Not proportional (different ratios).

2. For the second table:

   • \( \frac{10}{2} = 5 \)
   • \( \frac{20}{5} = 4 \)
   • \( \frac{30}{6} = 5 \)
   • Not proportional (different ratios).

3. For the third table:

   • \( \frac{2}{4} = 0.5 \)
   • \( \frac{3}{9} = \frac{1}{3} \approx 0.33 \)
   • \( \frac{4}{16} = 0.25 \)
   • Not proportional (different ratios).

4. For the fourth table:

   • \( \frac{2}{10} = 0.2 \)
   • \( \frac{3}{15} = 0.2 \)
   • \( \frac{8}{40} = 0.2 \)
   • Proportional (all ratios are equal).

Thus, the fourth table demonstrates a proportional relationship.