Question

Zachary purchases a computer for $1,400 on a payment plan. Four months after he purchased the computer, his balance was $820. Eight months after he purchased
the computer, his balance was $240. What is an equation that models the balance y after x

Answer 1

The equation that models the balance y after x is y = -145x + 1400

How to find the equation?

given that

Zachary uses a payment plan to buy a PC for $1,400. His balance was $820 four months after he made the computer purchase. His amount was $240 eight months after he made the computer purchase.

Assume it has to do with developing an equation that represents this loan as a function of time. Use the loan amount as Y and the time as X.

Now Put that in the standard format:

Y = mX + b

according to the question

at x = 0 then y = 1400

at x = 4 then y = 820

at x = 8 then y = 240

now find the slope

points are (4,820) & (8,240)

$slope = \frac{y2 - y1}{x2 - x1}$

$slope = \frac{240 - 820}{8 - 4}$

$slope = \frac{ - 580}{4}$

slope = -145

now the equation is y = -145x + b

Let x = 4 & y = 820

then

820 = -145(4) + b

820 = 580 + b

b = 820 + 580

b = 1400

finally the equation is

y = -145x + 1400

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