Question

Drag and drop the constant of proportionality into the box to match the table.

If the table is not proportional, drag and drop "not proportional" into the box.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x 0 3 6 9
y 0 2 4 6
The option "2" (4 of 5) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

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.)