Question

Cupcake World makes the best cupcakes of all kinds. The graph shows the relationship of cupcakes baked and additional cups of sugar used to bake the cupcakes.

The graph shows that the number of cupcakes baked are 30 and 50 with the additional cups of sugar is 10 and 20

What is the rate of change and what does it represent?

The rate of change is
, and represents

Answer 1

To find the rate of change based on the data provided, we can use the formula for the rate of change, which is given by:

\[
\text{Rate of Change} = \frac{\text{Change in Y}}{\text{Change in X}}
\]

In this scenario, we will let \( X \) represent the number of cupcakes baked and \( Y \) represent the additional cups of sugar used.

From the information provided:
- When 30 cupcakes are baked, 10 cups of sugar are used.
- When 50 cupcakes are baked, 20 cups of sugar are used.

This gives us two points:
- Point 1: (30, 10)
- Point 2: (50, 20)

Now, we can calculate the change in Y and the change in X:

\[
\text{Change in Y} = 20 - 10 = 10
\]
\[
\text{Change in X} = 50 - 30 = 20
\]

Now we can calculate the rate of change:

\[
\text{Rate of Change} = \frac{10}{20} = 0.5
\]

Thus, the rate of change is **0.5**.

**Interpretation**: The rate of change represents that for every additional cupcake baked, an extra 0.5 cups of sugar are needed.