Question

Does this show a proportional relationship between the number of boxes of lollipops and the cost in dollars?
Number of boxes of lollipops, x Cost in dollars, y
0 0
1 9
2 18
3 27
4 36

Yes

No

Answer 1

Yes, this shows a proportional relationship between the number of boxes of lollipops (x) and the cost in dollars (y).

In a proportional relationship, the ratio of y to x should remain constant. In this case:

- For 1 box: \( \frac{y}{x} = \frac{9}{1} = 9 \)
- For 2 boxes: \( \frac{18}{2} = 9 \)
- For 3 boxes: \( \frac{27}{3} = 9 \)
- For 4 boxes: \( \frac{36}{4} = 9 \)

The ratio is constant at 9, meaning that for every additional box of lollipops, the cost increases by $9. Therefore, it is a proportional relationship.