Question

Chung-Li is making cupcakes. He made the table below showing the amount of each ingredient needed for a certain number of cupcakes. Chung-Li plotted the data. He used the number of slices of strawberry as the x-coordinate and the number of slices of banana as the y-coordinate. He then drew a line to connect the points. Which point could be on the line that Chung-Li drew?

Number of Cupcakes Strawberries Slices of Banana
2 4 6
4 8 12
6 12 18
8 16 24
(1 point)
Responses

(1, 3)

(1, 3)

(3, 2)

(3, 2)

(2, 3)

(2, 3)

(1, 2)

Answer 1

To determine which point could be on the line that Chung-Li drew, we first need to identify the relationship between the number of slices of strawberries (x) and slices of bananas (y) based on the data provided.

From the table, we can observe the following pairs of strawberries and bananas:

- For 2 cupcakes: (4, 6)
- For 4 cupcakes: (8, 12)
- For 6 cupcakes: (12, 18)
- For 8 cupcakes: (16, 24)

Now, let's analyze the ratios of strawberries to bananas:

- From (4, 6), we can say that 4 slices of strawberries correspond to 6 slices of bananas.
- Therefore, the ratio is \( \frac{6}{4} = 1.5 \).
- Similarly, from (8, 12), we have \( \frac{12}{8} = 1.5 \).
- From (12, 18), \( \frac{18}{12} = 1.5 \).
- Finally, from (16, 24), \( \frac{24}{16} = 1.5 \).

The consistent ratio indicates that we have a linear relationship that can be described by the equation \( y = 1.5x \).

Now we can check each of the candidate points:

1. **(1, 3)**: If \( x = 1 \), then \( y = 1.5(1) = 1.5 \). This does not match (1, 3).

2. **(3, 2)**: If \( x = 3 \), then \( y = 1.5(3) = 4.5 \). This does not match (3, 2).

3. **(2, 3)**: If \( x = 2 \), then \( y = 1.5(2) = 3 \). This matches (2, 3).

4. **(1, 2)**: If \( x = 1 \), then \( y = 1.5(1) = 1.5 \). This does not match (1, 2).

Therefore, the point that could be on the line that Chung-Li drew is **(2, 3)**.