Question

proportianal relation ships in tables quick check

Answer 1

To determine proportional relationships in tables, you can follow these simple steps:

1. **Identify the Variables**: Look at the two columns in your table. Typically, one represents the independent variable (x) and the other the dependent variable (y).

2. **Calculate Ratios**: For each row, calculate the ratio of \( y \) to \( x \) (i.e., \( \frac{y}{x} \)).

3. **Check for Consistency**: If the same ratio is obtained for every row in the table, then \( y \) is proportional to \( x \) (i.e., they have a direct relationship).

4. **Identify the Constant of Proportionality**: If \( y \) is proportional to \( x \), the constant ratio (the result of \( \frac{y}{x} \)) is the constant of proportionality (k). The relationship can be expressed as \( y = kx \).

### Quick Example:

| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |

**Step 1**: Identify \( x \) and \( y \).
**Step 2**: Calculate ratios:
- \( \frac{3}{1} = 3 \)
- \( \frac{6}{2} = 3 \)
- \( \frac{9}{3} = 3 \)
- \( \frac{12}{4} = 3 \)

**Step 3**: Check for consistency: All ratios equal 3.
**Step 4**: Determine the constant of proportionality: \( k = 3 \).

Thus, the relationship between \( x \) and \( y \) can be expressed as \( y = 3x \).

### Summary:
- If the ratios \( \frac{y}{x} \) are consistent across the table, \( y \) is proportional to \( x \).
- The constant ratio is the constant of proportionality.