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Question 165387: This is my problem and I believe I have the answer (C(x))=3x+27,000 but I don't know the proper process for illustrating this. Please help!
# If the relationship between the total cost and the number of units produced is linear and if the total cost increases by $3 for each additional unit made:
1. Find the equation of the total cost function C(x) using the fact that C(1,000) = 30,000 (dollars) where x is the number of units produced.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since the "total cost increases by $3 for each additional unit made", this means that the slope is  . Also, because C(1,000) = 30,000 , this means that we have the point (1000,30000).
So let's find the equation of the line that has a slope of 3 and goes through the point (1000,30000)
If you want to find the equation of line with a given a slope of  which goes through the point (1000,30000), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
 where  is the slope, and ) is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in ,  , and  (these values are given)
 Distribute
 Multiply and  to get 
 Add 30000 to both sides to isolate y
 Combine like terms and  to get 
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Answer:
So the equation of the line with a slope of which goes through the point (1000,30000) is:
which is now in  form where the slope is and the y-intercept is 
So in function notation, the cost function is  . So you are correct.
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