Question

A business buys a computer for $3,000. After 4 years the value of the computer is expected to be $250. The value, v, can be related to the time in years, t, in a linear equation. Which equation models the relationship between v an t?
a.v=250t
b.v=-250t
c.v=687.50t-3,000
d.v=-687.50t+3,000

Answer 1

You are given two points in the linear function. At time 0 years, the value is $3000. At time 4 years, the value is $250. This means you have points (0, 3000) and (4, 250). You need to find the equation of the line that passes through those two points.

y = mx + b

m = (y2 - y1)/(x2 - x1) = (3000 - 250)/(0 - 4) = 2750/(-4) = -687.5

Use point (0, 3000).

3000 = -687.5(0) + b

b = 3000

The equation is

y = -687.5x + 3000

Since we are using points (t, v) instead of (x, y), we have:

v = -687.5t + 3000

Answer: d. v = -687.50 t + 3,000