Tim has a daily budget of $20 to spend on his morning coffee and everything else. The coffee shop he usually visits opens at 8 am and closes at 11 am. It sells one cup of coffee at a regular price of $4.5. Most people visit the coffee shop at 9 am, which makes the store very crowded, so the manager is considering a new promotion. For customers who order n minutes after 9 am, they can get 55n cents off the regular price for one cup of coffee. For those who order n minutes before 9 am, they can also get 55n cents off. For example, if Tim orders his coffee at 8:45 am, the price he is going to pay is just $3.75. This promotion is only valid for coffee orders between 8 am and 10 am.

Tim needs exactly one cup of coffee per day. Let t be the number of minutes between 8 am and when Tim orders his morning coffee. Let y denote the money that Tim spends on everything else. Write down the equations that represent combinations of t and y on Tim's budget line. (Hint: You need to discuss cases for different values of t.)