Question

Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was $1,440. Six months after he purchased the computer, his balance was $1,080. What is an equation that models the balance y after × months?

The equation __________ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)

Answer 1

Equation: y = 1800 - 120x

Explanation:

y = 1800 - mx Where x = months after purchase of computer

y = balance remaining

1800 = y-intercept because this is your initial balance remaining as it is the actual price of the computer.

The coefficient of ‘m’ will be negative for this equation because the value of y decreases as x increases. (NOTE: y is NOT indirectly proportional to x as the line of the equation does not pass through the origin)

Next step is to determine 'm’:

m = slope of equation

Two sets of x and y values have been provided:

`(x_(2), y_(2)) = (3, 1440)`

`(x_(3) ,y_(3))= (6, 1080)`

Use any set and substitute in the slope-intercept equation to determine the value of m:

1080 = 1800 - 6m

All the like terms are brought together and m needs to be isolated:

6m = 1800 - 1080

6m = 720

m =
`(720)/(6)`

m = 120

Therefore:

y = 1800 - 120x