Question

Identify the table that demonstrates a proportional relationship.(1 point) Responses x y 2 10 5 20 6 30x y 2 10 5 20 6 30 x y 10 2 15 3 40 8 x y 10 2 15 3 40 8 x y 8 2 12 3 40 4x y 8 2 12 3 40 4 x y 4 2 9 3 16 4

Answer 1

To identify a table that demonstrates a proportional relationship, we need to check if the ratio (y/x) remains constant for all pairs of x and y values in the table.

Let’s analyze each table:

1. **Table 1:**
- (2, 10) → 10/2 = 5
- (5, 20) → 20/5 = 4
- (6, 30) → 30/6 = 5
- Ratios are not constant → Not proportional.

2. **Table 2:**
- (10, 2) → 2/10 = 0.2
- (15, 3) → 3/15 = 0.2
- (40, 8) → 8/40 = 0.2
- Ratios are constant (0.2) → Proportional.

3. **Table 3:**
- (8, 2) → 2/8 = 0.25
- (12, 3) → 3/12 = 0.25
- (40, 4) → 4/40 = 0.1
- Ratios are not constant → Not proportional.

4. **Table 4:**
- (4, 2) → 2/4 = 0.5
- (9, 3) → 3/9 = 0.333
- (16, 4) → 4/16 = 0.25
- Ratios are not constant → Not proportional.

The only table that shows a proportional relationship is **Table 2**:
- x: 10, 15, 40; y: 2, 3, 8 where the ratio y/x = 0.2 for all pairs.