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

1 answer

To model the cost of the ice cream sundae with the topping options, we can create a mathematical expression based on the offer.

  1. Base Cost: The cost of the plain ice cream sundae is $4.
  2. Toppings Cost: Each topping costs $1, and you can choose from 0 to a maximum of 10 toppings.

The total cost (C) can be expressed as: \[ C = 4 + T \] where T is the number of toppings selected (T can take values from 0 to 10).

Thus, the total cost can range as follows:

  • If no toppings are chosen (T = 0), then \( C = 4 + 0 = 4 \).
  • If maximum toppings are chosen (T = 10), then \( C = 4 + 10 = 14 \).

This results in a cost range between $4 and $14.

Graphical Representation:

  • The cost would be a linear function starting from the point (0, 4) on the y-axis (when there are no toppings).
  • The slope of the line would be 1, as each topping adds $1 to the total cost.
  • The maximum point on the graph would be (10, 14).

The best graph to model this would be a line starting at (0, 4) and going up to (10, 14), forming a straight line with a slope of 1, and only defined for x values from 0 to 10 (the number of toppings).

When identifying the correct graph among options, look for:

  • A linear increase starting from $4.
  • A maximum point of $14 when there are 10 toppings.
  • No points below $4 or above $14 and only defined for integer values from 0 to 10.