50 points + 25 branilest john has $250 in his account and deposits $35 per month out of his lawn care money. construct a linear function that models john's bank balance for any given month

$250 - in his account

$35 per month out of (minus $35 per month from his account)

$250 - 1 · $35 - after the first month

$250 - 2 · $35 - after the second month

$250 - 3 · $35 - after the third month

...

n - the number of a month

The function:

Domain:

250 - 35n > 0      subtract 250 from both sides

-35n > -250      change the signs

35n < 250     divide both sides by 35

n < 7.142 → n < 8 → n ∈ {0, 1, 2, 3, 4, 5, 6, 7}

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.