Melanie buys 2 shells for $0.80. Rosi buys 3 shells for $1.20. Carlos buys 4 shells for $1.60. Use the graph to determine whether there is a proportional relationship between the number of shells and their cost. If so, what does the constant of proportionality mean in this situation? Use the drop-down menus to show and explain your answer.

Question

Gift shop shells graph showing cost in dollars on the y axis and number of shells on the x axis. A line begins at the origin and passes through the points 2 comma 80 cents, 3 comma 1 dollar and 20 cents, and 4 comma 1 dollar and 60 cents.

The relationship between the number of shells and their cost is
Choose...
.
The constant of proportionality means that each shell costs
Choose...

Answer 1

To determine whether there is a proportional relationship between the number of shells and their cost, we need to check if the ratio of cost to the number of shells is constant.

1. Melanie's purchase:

   • 2 shells cost $0.80
   • Cost per shell = \( \frac{0.80}{2} = 0.40 \) dollars per shell

2. Rosi's purchase:

   • 3 shells cost $1.20
   • Cost per shell = \( \frac{1.20}{3} = 0.40 \) dollars per shell

3. Carlos's purchase:

   • 4 shells cost $1.60
   • Cost per shell = \( \frac{1.60}{4} = 0.40 \) dollars per shell

Since the cost per shell remains constant at $0.40 for all purchases, we can conclude that:

• The relationship between the number of shells and their cost is proportional.

• The constant of proportionality means that each shell costs $0.40.