Question 73425
Since this is a linear equation by assumption, the slope-intercept form can be used.  This 
equation will be in the form y = mx + b.  But we will redefine the variables.  Replace
y with C the cost. x will still be used to represent the number of items produced. x will be on
the x-axis and C will be on the y-axis.
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As the number of items manufactured increases from 100 to 300 units (an increase of 200 items)
the cost goes from $10,000 to $22,000 (an increase of $12,000).  The slope of this graph is,
therefore:
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{{{12000/200= 60}}} 
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and the 60 represents the dollars that it costs to produce a unit.
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So far our equation is:
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{{{C = 60*x + b}}}
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The question now is how do we calculate b? We can use the fact that when x = 100, then
C = $10,000. Plug these values into the equation and you find:
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{{{10000 = 60*100 + b }}}
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This simplifies to:
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{{{10000 = 6000 + b}}}
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Subtract 6000 from both sides and you find that 
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{{{4000 = b}}}
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Plug that value into the equation and you get:
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{{{C = 60*x + 4000}}}
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This is the equation that relates C and x (thenCost and number of items produced).  
Notice something interesting.  If you produced no items (x = 0) the cost is still $4000.  
This probably involves the cost of labor to maintain the assembly line, store the materials, 
keep the lights and heat on, and so forth.  
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Hope this helps you to understand the graphing process.  You can check the equation out
by letting x = 300 items and see if the cost computes to $22,000 as specified in the problem.