Question 67116: Business and finance. In planning for a new item, a manufacturer assumes that
the number of items produced x and the cost in dollars C of producing these items
are related by a linear equation. Projections are that 100 items will cost $10,000 to
produce and that 300 items will cost $22,000 to produce. Find the equation that
relates C and x.
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Business and finance. In planning for a new item, a manufacturer assumes that
the number of items produced x and the cost in dollars C of producing these items
are related by a linear equation. Projections are that 100 items will cost $10,000 to
produce and that 300 items will cost $22,000 to produce. Find the equation that
relates C and x.
You are probably familiar with finding the equations of lines when you're given two points, (x1,y1) and (x2,y2). If so just change y1 and y2 into C1 and C2.
(x1,C1)=(100,10000) and (x2,C2)=(300,22000)
(It would make the numbers easier to deal with if you dealt with C in terms of 1000's and make C1=10 and C2=22. But I didn't want to confuse you, so I'm going with what you got. Your teacher may use 10 and 22 and note to the side that C is in terms of thousands.)
Any way the formula for the slope is:  , where m=slope and (x1.C1) and (x2,C2) are given points.
Now that you have a slope, you can use the point-slope formula:  , where m=slope and (x1,C1) is a given point, to find the equation.
m=60 and (x1,C1)=(100,10000)
There is another way to do this, if your teacher is using the slope intercept  , rather than the point-slope  . Let me know and I can show you that way.
Happy Calculating!!!
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