The Art Club collected $15 from each of its 17 members for dues. It then had $300 in its account. Assume the relationship is linear. Find and interpret the rate of change and the initial value.

The "rate of change" is presumed to refer to the rate at which the balance in the bank account changes as dues are collected from Art Club members. It increases by $15 for each new collection, so we can say ...

... the rate of change is $15 per member.

We further presume that the problem intends the "initial value" to refer to the fact that the 17 * $15 = $255 does not match the full amount of the current Art Club account balance ($300). So, there must have been some balance in the account before collection started. We can interpret that $45 "initial value" as ...

... the account balance before dues collection started is the initial value.