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
123not proportional223

Answer 1

To determine if the table represents a proportional relationship, we need to find the constant of proportionality (k) using the formula \( k = \frac{y}{x} \).

We can calculate it for the pairs of (x, y) values from the table:

• For (0, 0): \( k = \frac{0}{0} \) (undefined)
• For (3, 2): \( k = \frac{2}{3} \)
• For (6, 4): \( k = \frac{4}{6} = \frac{2}{3} \)
• For (9, 6): \( k = \frac{6}{9} = \frac{2}{3} \)

Since \( k \) is constant (equal to \( \frac{2}{3} \)) for the defined pairs (3, 2), (6, 4), and (9, 6), and we have \( k \) undefined at (0, 0), the relationship is proportional everywhere except for the undefined point.

Since it involves the point (0, 0) which is still considered a part of the line, we can conclude that the table is proportional.

Therefore, the constant of proportionality is \( \frac{2}{3} \).

Drag and drop \( \frac{2}{3} \) into the box for the constant of proportionality.