Question

Is the relationship between the values in the table a direct​ variation, an inverse​ variation, or​ neither?

Answer 1

To determine if the relationship between the values in a table represents direct variation, inverse variation, or neither, you'll need to analyze the data.

1. **Direct Variation**: This occurs when there is a constant ratio between two quantities. Mathematically, it can be expressed as \( y = kx \), where \( k \) is a non-zero constant. If you divide \( y \) by \( x \) (i.e., \( \frac{y}{x} \)), and this ratio remains constant for all pairs of values, then the relationship is a direct variation.

2. **Inverse Variation**: This occurs when the product of two quantities is a constant. Mathematically, it can be expressed as \( y = \frac{k}{x} \), where \( k \) is a non-zero constant. If you multiply \( x \) and \( y \) for all pairs of values and this product remains constant, then the relationship is an inverse variation.

3. **Neither**: If neither of the above conditions are satisfied, the relationship is neither direct nor inverse variation.

If you provide the specific values from the table, I can help you analyze them to determine the type of variation.