Question

peter deposited some money in a new checking account. over time, he withdrew the same amount of money each week to spend on movies and music. the table shows the balance in peter’s checking account, in dollars, over time.
time (t) balance (b)
4 weeks $537
8 weeks $449
10 weeks $405
15 weeks $295
how much money did peter deposit in his checking account?
$
complete the equation to represent the situation.
b = t +

Explanation:

Step1: Find the slope (weekly withdrawal)

Use two points, e.g., (4, 537) and (8, 449). Slope \( m = \frac{449 - 537}{8 - 4} = \frac{-88}{4} = -22 \).

Step2: Find the initial deposit (y-intercept)

Use point-slope form \( B - B_1 = m(t - t_1) \) with (4, 537) and \( m = -22 \).
\( B - 537 = -22(t - 4) \)
\( B - 537 = -22t + 88 \)
\( B = -22t + 625 \).
Initial deposit is when \( t = 0 \), so \( B = 625 \).

Answer:

Peter deposited \$625. The equation is \( B = -22t + 625 \).