Question

Pete's checking account showed a balance at the beginning of the month of 180. After 3 days, the checking account showed a balance of 172.50. Write a linear equation to represent the total in the checking account f(x) according to the day x?

Answer 1

To find the linear equation representing Pete's checking account balance, determine the rate of change and y-intercept from the given information. The equation is f(x) = -2.50x + 180, with a daily decrease of $2.50 in the balance.

Step-by-step explanation:

To write a linear equation that represents Pete's checking account balance according to the day, we need to start with the information given. Pete started with a balance of $180, and after 3 days, the balance is $172.50. This change in balance suggests Pete's account decreases by a certain amount each day, which can be represented by a straight line when graphed over time. Consequently, we can model the situation with a linear equation.

First, we need to determine the rate of change. The balance decreased by
$180 - $172.50 = $7.50 over 3 days, which means

the daily decrease is $7.50 / 3 = $2.50 per day.

Therefore, the slope (m) of our equation is -2.50 (negative because the balance is going down).

The initial balance, $180, is the y-intercept (b), the account balance when x (the number of days) is 0.

So the equation takes the standard linear form: y = mx + b.

The final linear equation representing Pete's checking account balance f(x) as a function of the day x is:

f(x) = -2.50x + 180