To determine the constant of proportionality from the given table, we first need to check if the relationship between \(x\) and \(y\) is proportional.
Given the table:
- When \(x = 0\), \(y = 0\)
- When \(x = 3\), \(y = 2\)
- When \(x = 6\), \(y = 4\)
- When \(x = 9\), \(y = 6\)
To check for proportionality, we look for a constant ratio \(k = \frac{y}{x}\):
- For \(x = 3\): \(k = \frac{2}{3}\)
- For \(x = 6\): \(k = \frac{4}{6} = \frac{2}{3}\)
- For \(x = 9\): \(k = \frac{6}{9} = \frac{2}{3}\)
The ratio is consistent across the values given in the table (as long as \(x \neq 0\)). Thus the constant of proportionality is \( \frac{2}{3} \) every time \(x\) is a non-zero value.
However, since \(x = 0\) produces \(y = 0\), it does not affect the proportional relationship as \(0\) divided by any number is still \(0\).
Since the relationship is indeed proportional,
The constant of proportionality is: 2/3.
(Note: You mentioned "2" is selected in your message. If "2" is the only choice available, I would suggest that you check if the options are correct since the computed constant should indeed be \( \frac{2}{3} \). If only "2" is possible, that might need clarification.)