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

Question

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.

1/2 3 not proportional 2 2/3

Answer 1

To determine if the table is proportional, we can find the constant of proportionality, which is the ratio of \( y \) to \( x \) for each pair of values.

Looking at the table:

• When \( x = 0 \), \( y = 0 \): the ratio is undefined, but we can ignore it in proportional calculations.
• When \( x = 3 \), \( y = 2 \): the ratio is \( \frac{2}{3} \).
• When \( x = 6 \), \( y = 4 \): the ratio is \( \frac{4}{6} = \frac{2}{3} \).
• When \( x = 9 \), \( y = 6 \): the ratio is \( \frac{6}{9} = \frac{2}{3} \).

The ratios are all equal (i.e., \( \frac{2}{3} \)).

Since the ratios are consistent, this table is proportional with a constant of proportionality of \( \frac{2}{3} \).

So, you would drag the constant of proportionality \( \frac{2}{3} \) into the box.