Question

2 - 5 additional practice

1. three friends are buying seashells at the gift shop on

the beach. melanle 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?

1. for each graph shown, tell whether it shows a proportional relationship.

explain why or why not.

1. the graph shows the relationship between

the distance a taxi travels and the cost
of the taxi ride. is the relationship
proportional? explain.

1. the graph shows a proportional

relationship between a familys distance
from home and the time spent driving.
a. what does the point (1, 49) represent?
b. look for relationships write
an equation that represents the
proportional relationship.

Explanation:

Step1: Calculate the unit rate for each friend

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

Step2: Analyze the graph

Since the unit rate (constant of proportionality) is the same ($0.40$) for all friends, when we plot the points (number of seashells, cost) \((2,0.80)\), \((5,2.00)\), \((4,1.60)\) on the graph, the line passing through these points will be a straight - line passing through the origin (because if \(x = 0\) (no seashells), \(y=0\) (no cost)).

for 2a:
A proportional relationship has a graph that is a straight line passing through the origin \((0,0)\). In graph \(a\), the line passes through the origin.

for 2b:
A proportional relationship has a graph that is a straight line passing through the origin \((0,0)\). In graph \(b\), the line does not pass through the origin.

for 3:
A proportional relationship has a graph that is a straight line passing through the origin \((0,0)\). In the "Cost of a Taxi Ride" graph, when \(x = 0\) (distance \(=0\) miles), \(y=3\) (cost is \(3\) dollars).

Answer:

Yes, the number of seashells and the cost have a proportional relationship. The constant of proportionality \(k = 0.40\). It means that each seashell costs \(0.40\) dollars.