Question

Describe how you know a table is proportional

Answer 1

A table is considered proportional if the relationship between the two quantities represented is constant. Here are several ways to determine if a table shows proportionality:

1. **Constant Ratio**: For each pair of values (x, y), calculate the ratio \( \frac{y}{x} \). If this ratio is the same for all pairs, the table represents a proportional relationship.

2. **Graphing**: If you plot the points from the table on a graph, proportional relationships will form a straight line passing through the origin (0,0).

3. **Zero Value**: If one value is zero, the corresponding value should also be zero. This is a characteristic of proportional relationships.

4. **Multiplicative Factor**: Check if you can find a constant \( k \) such that \( y = kx \) holds true for all pairs in the table. If you can express y in terms of x with a single constant, the relationship is proportional.

5. **Changes in Values**: If one quantity doubles, the other must also double to maintain proportionality. This can be observed through the changes in the values in the table.

By applying these methods, you can easily determine if the table represents proportional quantities.