Question

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

Answer 1

To determine if the quantities in a data table are in a proportional relationship, you should check if the ratios of the corresponding quantities are constant. A proportional relationship can be described as one where the relationship between two quantities is represented by the equation \(y = kx\), where \(k\) is a constant.

Here's a step-by-step guide to check if the quantities are proportional:

1. **Identify the Quantities**: Look at the pairs of quantities in your data table.

2. **Calculate Ratios**: For each pair, calculate the ratio of the two quantities. This can be done by dividing one quantity by the other.

3. **Check for Consistency**: If all the calculated ratios are equal (or very close, considering rounding errors), then the two quantities are proportional. If the ratios vary, then they are not proportional.

4. **Example**:
- If your data table has pairs such as (1, 2), (2, 4), (3, 6), calculate:
- For (1, 2): Ratio = 2/1 = 2
- For (2, 4): Ratio = 4/2 = 2
- For (3, 6): Ratio = 6/3 = 2
- Since all ratios are equal (2), these quantities are in a proportional relationship.

If you provide the specific data table, I can help you with that analysis directly!