Identify the table that demonstrates a proportional relationship.(1 point)%0D%0AResponses%0D%0A%0D%0Ax%09y%0D%0A10%092%0D%0A15%093%0D%0A40%098%0D%0A %0D%0A%0D%0Ax y 10 2 15 3 40 8 %0D%0A%0D%0Ax%09y%0D%0A8%092%0D%0A12%093%0D%0A40%094

Answer 1

To determine which table demonstrates a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) remains constant for each pair of \( (x, y) \).

Let's analyze both tables provided.

Table 1:

x   |  y
10  |  2
15  |  3
40  |  8

Now, we calculate the ratios \( \frac{y}{x} \):

• For \( (10, 2) \): \( \frac{2}{10} = 0.2 \)
• For \( (15, 3) \): \( \frac{3}{15} = 0.2 \)
• For \( (40, 8) \): \( \frac{8}{40} = 0.2 \)

The ratio \( \frac{y}{x} \) is constant (0.2) for all pairs, so this table demonstrates a proportional relationship.

Table 2:

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

Now, we calculate the ratios \( \frac{y}{x} \):

• For \( (8, 2) \): \( \frac{2}{8} = 0.25 \)
• For \( (12, 3) \): \( \frac{3}{12} = 0.25 \)
• For \( (40, 4) \): \( \frac{4}{40} = 0.1 \)

The ratio is not constant (0.25 for the first two pairs and 0.1 for the last), so this table does not demonstrate a proportional relationship.

Conclusion: The first table demonstrates a proportional relationship.