Question

the table shows the relationship between the number of months music is streamed and the cost of a music streaming service. which equation shows the same relationship?
number of months, m | cost, c (in dollars)
2 | 5
5 | 12.5
8 | 20
12 | 30
options: c = \frac{2.5}{m}, c = 2.5m, c = \frac{5}{m}, c = 5m

Explanation:

Step1: Identify the relationship type

We check if the relationship between \( m \) (months) and \( C \) (cost) is proportional. For proportional relationships, \( \frac{C}{m} \) should be constant.

Step2: Calculate \( \frac{C}{m} \) for each row

• For \( m = 2 \), \( C = 5 \): \( \frac{5}{2} = 2.5 \)
• For \( m = 5 \), \( C = 12.5 \): \( \frac{12.5}{5} = 2.5 \)
• For \( m = 8 \), \( C = 20 \): \( \frac{20}{8} = 2.5 \)
• For \( m = 12 \), \( C = 30 \): \( \frac{30}{12} = 2.5 \)

Since \( \frac{C}{m} = 2.5 \) (constant), the equation is \( C = 2.5m \).

Answer:

\( C = 2.5m \)