Write A Linear Equation

[nycmathguy]

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 me see.

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.

Correct?

 

[MathLover1]

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 me see.

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.


Let the time in years after the equipment
was bought = t,
Let V = the value of the equipment at any point in time

When t = 0 , V[0] = 24000
When t = 10 , V[10] = 2000

The equation to use is
(V - V[0])/(t- t[0]) = (V[10] - V[0])/(t[10] - t[0])
(V - 24000)/(t - 0) = (2000 - 24000)/(10 - 0)
(V - 24000)/t = -22000/10
V - 24000 = -2200t
V = -2200t + 24000->answer

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.

Correct?

 

[nycmathguy]

Thanks. I got it right.