Paying the rent
Task
A checking account is set up with an initial balance of \$4800, and \$400 is removed from the account each month for rent (no other transactions occur on the account).
 Write an equation whose solution is the number of months, $m$, it takes for the account balance to reach \$2000.
 Make a plot of the balance after $m$ months for for $m=1,3,5,7,9,11$ and indicate on the plot the solution to your equation in part (a).
IM Commentary
This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.
Solution
 Since the account starts with \$4,800 and decreases by \$400 each month, there will be $4800400m$ dollars left in the account after $m$ months have passed. The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is $$ 4800400m=2000. $$

The following table collects the relevant data points.
$m$ (months) 1 3 5 7 9 11 Balance $4800400m$ 4400 3600 2800 2000 1200 400 Balance in an account 1â€“11 months after its establishment As is found in the table or by solving the equation in part (a), the balance in the account is \$2,000 after 7 months. The point $(7,2000)$, and a dashed line plotting the more general relationship, is indicated in the graph below:
Paying the rent
A checking account is set up with an initial balance of \$4800, and \$400 is removed from the account each month for rent (no other transactions occur on the account).
 Write an equation whose solution is the number of months, $m$, it takes for the account balance to reach \$2000.
 Make a plot of the balance after $m$ months for for $m=1,3,5,7,9,11$ and indicate on the plot the solution to your equation in part (a).