At the beginning of the summer Conan has $180 in the bank each week he deposits another $64 that he earns mowing lawns is his account balance proportional to the number of weeks since he started mowing lawns
For the balance to be directly proportional, we must have an equation with no constant
Bal = 64w
but we have Bal = 64w + 180
Looking at y = mx + b
y would not be proportional to x, because of the constant b
whereas y = mx is a direct proportion, or we can say that y is proportional to x
To determine if Conan's account balance is proportional to the number of weeks, we need to check if there is a constant ratio between his account balance and the number of weeks.
We can calculate Conan's account balance for different numbers of weeks and see if the ratio between the balance and weeks remains constant.
Let's start by calculating the account balance for the first few weeks:
Week 1:
Conan's initial balance: $180
Additional deposit: $64
Total balance = $180 + $64 = $244
Week 2:
Conan's previous balance: $244
Additional deposit: $64
Total balance = $244 + $64 = $308
Week 3:
Conan's previous balance: $308
Additional deposit: $64
Total balance = $308 + $64 = $372
We can continue this calculation for a few more weeks. For each week, we add the additional deposit to the previous balance to get the new balance.
Now, let's calculate the ratios between Conan's account balance and the number of weeks for the first few weeks:
Week 1: Ratio = $244 / 1 = $244
Week 2: Ratio = $308 / 2 = $154
Week 3: Ratio = $372 / 3 = $124
As we can see, the ratios between the account balance and the number of weeks are not constant. Therefore, Conan's account balance is not proportional to the number of weeks since he started mowing lawns.