Question

three friends are buying seashells at the gift shop on the beach. melanie buys 2 seashells for $0.80. rosi buys 5 seashells for $2.00. carlos buys 4 seashells for $1.60. use a graph to determine whether the number of seashells and the cost have a proportional relationship. if so, what is the constant of proportionality and what does it mean? click the icon to view the blank graph. choose the correct graph below. oa. ob. oc. od. view an example video get more help - clear all check answer

Explanation:

Step1: Calculate the unit price for each person

For Melanie: The cost per seashell is $\frac{0.80}{2}=0.40$ dollars per seashell.
For Rosi: The cost per seashell is $\frac{2.00}{5} = 0.40$ dollars per seashell.
For Carlos: The cost per seashell is $\frac{1.60}{4}=0.40$ dollars per seashell.

Step2: Analyze the proportional relationship

Since the cost per seashell (unit rate) is the same ($k = 0.40$) for all three friends, the relationship between the number of seashells ($x$) and the cost ($y$) is proportional. The equation of a proportional relationship is $y=kx$, where $k$ is the constant of proportionality.

Step3: Analyze the graph characteristics

A proportional relationship has a straight - line graph that passes through the origin $(0,0)$. The slope of the line (which is equal to the constant of proportionality) is positive.

Answer:

The constant of proportionality is $k = 0.40$. It means that each seashell costs $0.40$ dollars. The correct graph is the one that is a straight line passing through the origin with a positive slope (assuming graph C is the one that meets these criteria as we don't have the actual visual labels for the graphs in a detailed way, but based on the calculation of a constant unit rate and the properties of a proportional relationship graph (straight line through the origin)).