The business manager says that it costs $320 to produce 100 CDs and $400 to produce 500 CDs.

Question

Write a linear function in point-slope form that represents the cost, $C, of producing n CDs.

Answer 1

Based on the data provided, we know that 400 CDs (500-100) can be produced for $80 (400-320).  So each CD costs $0.20 (80/400), not counting the cost of setting up the process.  The slope (m) is 0.20, and we must find the setup cost, or y-intercept (b).  We can use either data point to do this.

 

y = mx + b

320 = (0.20 * 100) + b
320 = 20 + b

b = 300

 

400 = (0.20 * 500) + b

400 = 100 + b

b = 300

 

The final equation for total cost (C) given the number of CDs to be produced (x) is:

 

C = 0.20 x + 300