How Do You Form a Linear Equation for the Equipment's Value Over 10 Years?

[nycmathguy]

Homework Statement

Write a linear equation representing the situation at hand.

Relevant Equations

y = mx + b

A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use.

Let t = time

The general linear equation representing this situation is V = mt + b.

I will reduce 24,000/2,000 to the lowest terms.

24,000/2,000 becomes 24/2.

Slope = (change in V)/(change in t).

Slope = (2 - 24)/(10 - 0)

Slope = -20/10

Slope = -2.

I now go back to the general linear equation given above to plug -2 for m (the slope) and 24 for b (our y-intercept).

I say the equation is V = -2t + 24.

You say?

 

[PeroK]

I ask how much is it worth after 10 years?

 

[Mark44]

I say the equation is V = -2t + 24.

So the equipment is worth $24 at the beginning (at t = 0)?

 

[TonyStewart]

Slope = (2 - 24)/(10 - 0) = 2

I say the equation is V = -2t + 24.

You say?

Always Validate your answer.
you meant 22/10 = 2.2

for t= 10 , V=2, a = (2-24)/10 = -2.2 thus V = -2.2t+24 for units in [$k]