SOLUTION: In planning for a new item, a manufacturer assumes that the number of items prduced x and the cost in dollars C of producing these items are related by linear equation. Projections

Question 69565: In planning for a new item, a manufacturer assumes that the number of items prduced x and the cost in dollars C of producing these items are related by 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 Earlsdon(6098) (Show Source):
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This is just like writing the equation of a line that passes through two given point. You can treat the cost variable, C as the dependent variable abd the number of items variable, x as the independent variable.
THe equation can be in the slope-intercept form:

Let's first find the slope using the two given points: (100, 10,000) and (300, 22,000)
Simplifying this we get:

So, we can write:
So now we need to find the value of b. We can do this by substituting one set of the given values for x and C (x, C) = (100, 10,000) and solve for b.
Simplifying, we get:
Subtracting 6000 from both sides, we get:
Now we can write the complete equation relating the cost, C and the number of items produced, x.
This is the required linear equation!