Final answer:
To write a proportional equation for the total cost in terms of the number of songs downloaded, one would typically use c = k*s, where k is the cost per song. However, with inconsistent costs provided in the question, it is not possible to determine an accurate constant rate without further correct information.
Step-by-step explanation:
To establish a proportional equation that represents the total cost, c, in terms of the number of songs downloaded, s, we must observe the given cost for each song. Given that songs cost $6.58, $8.46, and $9.40, these numbers appear unrelated at first glance, which would not lead to a single constant rate. However, as there might be a mathematical error in the costs and number of songs provided, we will assume there is a constant rate of cost per song.
Assuming a consistent cost per song, the proportional relationship between total cost and the number of songs downloaded can normally be represented by c = k·s, where k is the constant rate of cost per song. To find the value of k, we would need a correct pair of values for c and s. As it is now, we do not have enough information to define k.
If we had a consistent cost per song, and let's assume it is $1.50 for the purpose of an illustration, the equation would be c = $1.50·s. This equation implies that for every song downloaded, the cost increases by $1.50.