Question

For tax purposes, a business depreciates its $360,000 building using "straight-line depreciation" over 18 years by reducing its value by 1/18 of its original value each year. If we assume that the value of the building can be found or estimated at any point of time during this period, the value of the building can be modeled by the function y=360,000−20,000x, where x is the number of years. Complete parts (a) through (c).

Answer 1

We have the function:

• y= 360,000 - 20,000x

Where x is the number of years.

Slope-intercept form equation:

y= mx + b

Where:

m= slope

b= y-intercept ( where the line crosses the y axis)

So, for the equation given:

y= -20,000x + 360,000

a) The y-intercept is: 360,000

This means that at the beginning of the 18 years, the building is worth $360,000.(B)

For x= 0 ( at the beginning is year 0 )

y= 360,000 - 20,000 (0)

y= 360,000

b)

To find the x-intercept replace y= 0

y= -20,000x + 360,000

0 = -20,000x + 360,000

20,000x = 360,000

x= 360,000/20,000

x= 18

The x-intercept is 18

This means that the value of the building is 0 (zero) at the end of the 18 years.(A)

Replacing x= 18

y= 360,000 - 20,000(18)

y= 360,000-360,000

y= 0

c) Since the intercepts are:

y= 360,000

x= 18

The correct graph of the function is graph C