Question

After it is purchased, the value of a new car decreases $4,000 each year. After 3 years the car is worth $18,000. Which equation shows the value of the car in x years? A. y = 4000x + 18,000B. y = -4000x + 18,000C. y = -4000x + 30,000D. None of the above

Answer 1

y = 7000x - 3000

Step-by-step explanation:

let the amount of years be x

Let the price of car be y

If the value of a new car decreases $4,000 each year, this means that;

when x = 1, y = 4000.

In coordinate form (1, 4000)

If after 3 years the car is worth $18,000, this means that;

when x = 3, y = 18000

In coordinate form (3, 18000)

The equation in linear form is expressed as y = mx+c

m is the rate of change (slope)

c is the intercept

Get the slope

m = y2-y1/x2-x1

m = 18000-4000/3-1

m = 14000/2

m = 7000

Get the intercept c;

Substitute m = 7000 and any point say (1, 4000) into the formula y = mx+c

4000 = 7000(1) + c

4000 - 7000 = c

c = -3000

Get the linear equation

Recall that y = mx+c

y = 7000x - 3000