Jackie is selling smoothies at a school fair. She starts the day with $15 in her cash box to provide change to her customers. If each smoothie costs $3.75, which graph represents the balance of the cash box, y, after Jackie sells x smoothies?

To find the correct graph that represents the balance of Jackie’s cash box after selling smoothies, we need to calculate how the balance changes as she sells smoothies.

1. Jackie starts with $15.
2. Each smoothie costs $3.75.
3. For each smoothie sold, her cash box increases by $3.75.

Let’s define the relationship mathematically:

- If **x** is the number of smoothies sold, then the cash box balance, **y**, after selling **x** smoothies can be calculated as:
\[
y = 15 + 3.75 \cdot x
\]

Now, we can calculate the balance for a few values of **x**:

- For **x = 0**:
\[
y = 15 + 3.75 \cdot 0 = 15
\]

- For **x = 2**:
\[
y = 15 + 3.75 \cdot 2 = 15 + 7.5 = 22.5
\]

- For **x = 4**:
\[
y = 15 + 3.75 \cdot 4 = 15 + 15 = 30
\]

- For **x = 6**:
\[
y = 15 + 3.75 \cdot 6 = 15 + 22.5 = 37.5
\]

- For **x = 8**:
\[
y = 15 + 3.75 \cdot 8 = 15 + 30 = 45
\]

- For **x = 10**:
\[
y = 15 + 3.75 \cdot 10 = 15 + 37.5 = 52.5
\]

- For **x = 12**:
\[
y = 15 + 3.75 \cdot 12 = 15 + 45 = 60
\]

- For **x = 14**:
\[
y = 15 + 3.75 \cdot 14 = 15 + 52.5 = 67.5
\]

- For **x = 16**:
\[
y = 15 + 3.75 \cdot 16 = 15 + 60 = 75
\]

Now we can summarize the points calculated:
- (0, 15)
- (2, 22.5)
- (4, 30)
- (6, 37.5)
- (8, 45)
- (10, 52.5)
- (12, 60)
- (14, 67.5)
- (16, 75)

Since the cash box balance starts at $15 and increases consistently based on the number of smoothies sold, we compare our results with the provided options:

- Option C lists the points: (0, 15), (2, 22.5), (4, 30), (6, 37.5), (8, 45), (10, 52.5), (12, 60), (14, 67.5), and (16, 75).

Therefore, the correct answer is **C**.