Question
Jamie is icing cupcakes for his birthday party. He is careful about using the same amount of icing on each cupcake. There is a linear relationship between the number of cupcakes Jamie iced and the amount of icing he has used, in cups. 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 x y Number of cupcakes Amount of icing (cups) Describe the rate of change for this relationship. The amount of icing Jamie used increased decreased by 1 4 of cup 1 3 of a cup 2cups 4cups 6cups 8cups per cupcake.
Answers
GPT-4o mini
To determine the rate of change in this linear relationship, we need to analyze the data provided.
The values for the number of cupcakes (x) and the amount of icing (y in cups) are presented in a consistent pattern:
- When Jamie iced 2 cupcakes, he used 2 cups of icing.
- When he iced 4 cupcakes, he used 4 cups of icing.
- Continuing this, for every increase of 2 cupcakes, he used 2 additional cups of icing.
From this pattern, we can say:
- For every 2 cupcakes, the amount of icing increases by 2 cups.
To find the rate of change per cupcake, we can express this relationship by calculating the change in icing per cupcake:
\[
\text{Rate of change} = \frac{\text{Change in icing (cups)}}{\text{Change in cupcakes}} = \frac{2 \text{ cups}}{2 \text{ cupcakes}} = 1 \text{ cup per cupcake}
\]
Thus, the correct description of the rate of change for this relationship is:
**The amount of icing Jamie used increased by 1 cup per cupcake.**
The values for the number of cupcakes (x) and the amount of icing (y in cups) are presented in a consistent pattern:
- When Jamie iced 2 cupcakes, he used 2 cups of icing.
- When he iced 4 cupcakes, he used 4 cups of icing.
- Continuing this, for every increase of 2 cupcakes, he used 2 additional cups of icing.
From this pattern, we can say:
- For every 2 cupcakes, the amount of icing increases by 2 cups.
To find the rate of change per cupcake, we can express this relationship by calculating the change in icing per cupcake:
\[
\text{Rate of change} = \frac{\text{Change in icing (cups)}}{\text{Change in cupcakes}} = \frac{2 \text{ cups}}{2 \text{ cupcakes}} = 1 \text{ cup per cupcake}
\]
Thus, the correct description of the rate of change for this relationship is:
**The amount of icing Jamie used increased by 1 cup per cupcake.**