# Using linear depreciation, how do you determine the value of a machine after 5 years if it costs $62310 when new and has a value of$32985 after 7 years?

The value of the machine after $5$ years is $41364 #### Explanation: Initial cost of the machine is y_1=$62310.00 , x_1=0
Depriciated value of the machine after ${x}_{2} = 7$ years is
y_2=$32985.00 .Linear depriciation slope per year is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \mathmr{and} m = \frac{32985.00 - 62310.00}{7 - 0}$$m = \frac{32985.00 - 62310.00}{7}$. Depriciated value of the machine after $x = 5$years is $y - {y}_{1} = m \left(x - {x}_{1}\right)$or $y - 62310 = \frac{32985.00 - 62310.00}{7} \cdot \left(5 - 0\right)$or $y = 62310 + \frac{32985.00 - 62310.00}{7} \cdot 5$or y=62310-20946.43 or y ~~$41363.57 ~~ $41364 The value of the machine after $5$years is $41364