Question

Determine if the quantities in the data table are in proportional relationship

Answer 1

To determine if the quantities in a given data table are in a proportional relationship, you need to check if the ratio of one quantity to another remains constant throughout the table.

Here's a general step-by-step method to check for proportional relationships:

1. **Identify the pairs of quantities**: Look at the two columns (or more) of data that you want to compare.

2. **Calculate the ratios**: For each pair of values, calculate the ratio by dividing one quantity by the other.

3. **Check for consistency**: See if all the calculated ratios are the same. If they are, then the quantities are in a proportional relationship. If not, they are not proportional.

**Example**:
Consider a data table with the following values:

| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

1. **Calculate the ratios**:
- 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): \( \frac{y}{x} = \frac{8}{4} = 2 \)

2. **Check for consistency**: Since all the ratios are equal to \( 2 \), the quantities are in a proportional relationship.

If you provide the specific data table you have, I'd be happy to help you determine if they form a proportional relationship!