Question 37269This question is from textbook Beginning Algebra
: I have not a clue how to solve this. I am horrible at Algebra, PLEASE HELP!!!!
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.
This question is from textbook Beginning Algebra
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! They make it sound so darn difficult, huh? Let me show you...
They give us two data points for x and C, that is (x, C) as
(100, 10000) and (300, 22000)
Just like with any x and y, we first find the slope and then use the point-slope form of a line...so slope m is
m = (y2 - y1) / (x2 - x1) = (22000 - 10000) / (300 - 100) =
m = 12000 / 200 = 60
Now that we know m = 60, we use
y - y1 = m(x - x1) which is the point-slope form. In our problem however, the y is or C...so we have (using either (x, C))...
C - 10000 = 60(x - 100)
C - 10000 = 60x - 6000 and finally
C = 60x + 4000
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