Question

1. cars :

after a car is purchased, the value of it decreases $4,000 each year. after 3 years, the car is worth $18,000.

a) write an equation that represents the value v (in dollars) of the car x years after it is purchased.

b) what was the original value of the car?

Explanation:

Step1: Identify linear form

The value follows $V = mx + b$, where $m=-4000$ (annual decrease).

Step2: Substitute known point

Plug $x=3$, $V=18000$, $m=-4000$ into the equation:
$18000 = -4000(3) + b$

Step3: Solve for initial value $b$

Calculate $-4000(3) = -12000$, then:
$b = 18000 + 12000 = 30000$

Step4: Write the full equation

Substitute $m=-4000$ and $b=30000$ into $V = mx + b$.

Answer:

a) $V = -4000x + 30000$
b) $\$30,000$