Question

In August 2009, the classified ads for used cars listed a 3-year old Cadillac for $24,000

and an 11-year old Cadillac for $8,000. Assume that the depreciation is linear.
Write a linear equation that gives the value of the car, V, for the age of the car, a.​

Answer 1

`V=-2,000a+30,000`

Explanation:

Let V be the value of the car and a be the age of the car.

When a = 3, V = $24,000. So, we get the point (3, 24,000).

When a = 11, V = $8,000. So, we get the point (11, 8,000).

Write the equation of the line passing through these points:

`(V-8,000)/(24,000-8,000)=(a-11)/(3-11)\\ \\(V-8,000)/(16,000)=(a-11)/(-8)\\ \\V-8,000=-(16,000)/(8)(a-11)\\ \\V-8,000=-2,000(a-11)\\ \\V=-2,000a+22,000+8,000\\ \\V=-2,000a+30,000`