Question

1. there is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. the cost for 6 months is $47.94. the point (6, 47.94) is shown on the graph below.

a. what is the constant of proportionality in this relationship?
b. what does the constant of proportionality tell us about the situation?
c. add at least three more points to the graph and label them with their coordinates.
d. write an equation that represents the relationship between c, the total cost of the subscription, and m, the number of months.

Explanation:

Step1: Find the constant of proportionality

The formula for the constant of proportionality \( k \) in a proportional relationship \( y = kx \) (here \( C=km \)) is \( k=\frac{y}{x} \). Given the point \((6,47.94)\), where \( x = 6\) (months) and \( y=47.94\) (cost). So \( k=\frac{47.94}{6}\).
$$k = 7.99$$

Step2: Interpret the constant of proportionality

The constant of proportionality \( k = 7.99\) means that for each month of the streaming - movie subscription, the cost is \( \$7.99\).

Step3: Find additional points

Using the equation \( C = 7.99m\):

• When \( m = 1\), \( C=7.99\times1 = 7.99\), so the point is \((1,7.99)\)
• When \( m = 2\), \( C=7.99\times2=15.98\), so the point is \((2,15.98)\)
• When \( m = 3\), \( C=7.99\times3 = 23.97\), so the point is \((3,23.97)\)

Step4: Write the equation

Since \( C\) (total cost) and \( m\) (number of months) are in a proportional relationship \( C = km\), and \( k = 7.99\), the equation is \( C=7.99m\)

Answer:

a. The constant of proportionality is \( 7.99\).
b. It means the cost per month of the subscription is \(\$7.99\).
c. Points: \((1,7.99)\), \((2,15.98)\), \((3,23.97)\) (answers may vary depending on the values of \(m\) chosen).
d. The equation is \(C = 7.99m\)