Question

Need help solving this problem Value of a Copy Machine. Cassandra buys a new color copier for her small business. It will cost $21,000 and will decrease in value each year. The graph below shows the value of the copier after the first 5 years of ownership.

Answer 1

a. The copier will be worth $6,000 after 5 years.

b. It will be worth $12,000 after 3 years.

c. The slope of this line is -3000.

d. The copier decreased $3,000 in value per year.

e. An equation of this line is V = -3000x + 21000.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;

y = mx + b

Where:

• m represents the slope or rate of change.
• x and y are the points.
• b represents the y-intercept or initial value.

Part a.

Based on the graph, the line passes through the point (5, 6). Therefore, the copier will be worth $6,000 after 5 years.

Part b.

Based on the graph, the line passes through the point (3, 12). Therefore, the copier will be worth $12,000 after 3 years.

Part c.

The slope of any straight line can be determined by using the following mathematical equation;

Slope(m) =
`(y_2-y_1)/(x_2-x_1)`

Slope(m) = (12000 - 21000)/(3 - 0)

Slope(m) = -9000/3 = -3000.

Part d.

Since the slope of the line is -3000, it means that the copier decreased $3,000 in value per year.

Part e.

An equation of this line can be written as follows;

y = mx + b

V = -3000x + 21000

where;

V is the value after t years.

Answer 2

a)

Look for the intersection between the graph of the function and x=5. Then, after 5 years, the copier is worth 6*$1000=$6000. The answer to part a) is $6000

b)

Look for the intersection between the graph and y=12; thus, the answer to part b) is 3 years.

c) The line goes through (0,21000), and (1,18000); thus, the slope of the line is

`\begin{gathered} (0,21000),(1,18000) \\ \Rightarrow m=(21000-18000)/(0-1)=-3000 \end{gathered}`

The slope of the line is -3000.

d) According to the value of the slope of the line, The copier decreased by $3000 in value per year.

e) In general, the equation of the line is given by the formula below,

`\begin{gathered} V=mt+b \\ m\rightarrow slope \\ b\rightarrow y-intersection \end{gathered}`

From part c), we already know m. As for b, notice that the intersection between the line and the y-axis is (0,21000); therefore,

`\begin{gathered} m=-3000,b=21000 \\ \Rightarrow V=-3000t+21000 \end{gathered}`

The answer to part e) is V=-3000t+21000