A copy Machine

Question

A copy machine you purchased for your business in 2012 cost 1200 dollars. In 2013, you find thtat the value has depreciated to 960 dollars. Using the idea of linear depreciation, write the equation for the value v of this machine over n years since 2010. First list two points for (n,v) and then write the linear equation. Give your final equation in slope-intercept form. 

 

Two points:

 

Final equation:

Answer 1

The two points in format (n, v) are (0, 1200) and (1, 960). For n is the number of years since purchase date and v is the value of the copier. For example, the machine was purchased in 2012, which means n is 0 for the year 2012, 1 for the year 2013, 2 for the year 2014 so on and so forth. 

 

From 2 points, you can find the slope (rise over run or change of y over change in x in this case, it's change of v over change in n) 

slope = (960-1200)/(1-0) = -240

 

Now, write the equation in the point-slope form picking either point of the two. I picked (0, 1200) to be my (x₀,y₀)

y-y₀ = m(x-x₀)

y-1200 = -240(x-0)

 

Then convert to slope-intercept form using algebra

y-1200 = -240x+0

y = -240x+1200

 

Answer: The equation is v = -240n +1200 in slope-intercept form (y = mx+b)