Question

proportianal relationships in tables practice

Answer 1

Proportional relationships are situations where two quantities maintain a constant ratio. When represented in tables, the values of one quantity will always be proportional to the values of another quantity. Below are some practice problems that involve identifying and working with proportional relationships in tables.

### Example Table

| \(x\) | \(y\) |
|-------|-------|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |

**Q1**: Verify if the relationship between \(x\) and \(y\) is proportional.

To do this, calculate the ratio \( \frac{y}{x} \) for each pair. If the ratio is constant, then it is a proportional relationship.

### Q1 Answer
- **For (1, 2)**: \( \frac{y}{x} = \frac{2}{1} = 2\)
- **For (2, 4)**: \( \frac{y}{x} = \frac{4}{2} = 2\)
- **For (3, 6)**: \( \frac{y}{x} = \frac{6}{3} = 2\)
- **For (4, 8)**: \( \frac{y}{x} = \frac{8}{4} = 2\)
- **For (5, 10)**: \( \frac{y}{x} = \frac{10}{5} = 2\)

Since all ratios are equal to 2, the relationship is proportional.

### Practice Problems

#### Problem 1

| \(x\) | \(y\) |
|-------|-------|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |

1. Check if the relationship is proportional.
2. What is the constant of proportionality?

#### Problem 2

| \(x\) | \(y\) |
|-------|-------|
| 2 | 6 |
| 4 | 10 |
| 6 | 14 |
| 8 | 18 |
| 10 | 22 |

1. Check if the relationship is proportional.
2. If it is not proportional, describe the relationship.

#### Problem 3

| \(x\) | \(y\) |
|-------|-------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |

1. Determine if the relationship is proportional.
2. Find the formula relating \(x\) and \(y\).

### Answers

#### Problem 1
1. Yes, it's proportional.
2. The constant of proportionality is 5.

#### Problem 2
1. No, it's not proportional.
2. The relationship is linear, and can be described by the equation \(y = 2x + 2\).

#### Problem 3
1. Yes, it is proportional.
2. The formula relating \(x\) and \(y\) is \(y = 3x\).

Feel free to try these problems or ask for additional scenarios!