Final answer:
A linear equation representing the scenario where a checking account balance decreases daily from a starting balance of $180 to $172.50 after 3 days is y = -2.50x + 180.
Step-by-step explanation:
To write a linear equation representing the scenario where a checking account starts off with $180 and shows a balance of $172.50 after 3 days, we can assume that the account is reducing by a fixed amount every day. Let's denote the balance as y and the number of days as x. The starting balance when x=0 is $180. After 3 days (x=3), the balance is $172.50.
To find the daily change, we calculate the difference between the starting balance and the balance after 3 days, which is $180 - $172.50 = $7.50. Since this change happened over 3 days, we divide by 3 to find the change per day: $7.50 / 3 = $2.50. Therefore, the balance decreases by $2.50 each day.
Now, we can set up the linear equation as y = -2.50x + 180, where y is the balance of the checking account, and x is the number of days since the beginning of the month.