Question

The local ice cream shop offers a deal on Wednesday where you can pay $4 for a plain ice cream sundae and $1 per topping you choose (maximum of 10 toppings). Which of the following graphs best models the cost someone could pay using this offer? (1 point)
Responses

Answer 1

To model the cost of the ice cream sundae based on the number of toppings, we can define the cost function mathematically.

The cost \( C \) can be expressed as:
\[ C = 4 + (1 \times n) \]
where \( n \) is the number of toppings, which can range from 0 to 10.

This means:
- If no toppings are chosen (\( n = 0 \)), the cost is \( C = 4 + 0 = 4 \).
- If 1 topping is chosen (\( n = 1 \)), the cost is \( C = 4 + 1 = 5 \).
- If 10 toppings are chosen (\( n = 10 \)), the cost is \( C = 4 + 10 = 14 \).

The graph representing this cost would start at the point (0, 4) on the y-axis and will be a straight line with a slope of 1 (since each topping increases the cost by $1), ending at the point (10, 14).

So, the key features of the graph would be:
- A y-intercept at (0, 4)
- A slope of 1, indicating that the cost increases by $1 for each topping
- The x-axis representing the number of toppings (ranging from 0 to 10)
- The y-axis representing the total cost (ranging from $4 to $14)

Choose the graph that reflects these characteristics.