The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4000 to produce 300 chairs in one day.

b)What is the slope of the line in part (a), and what does it represent?

C = m c + b

Where C is the cost of production and c is the number of chairs produced.

Using the given data

2200 = 100m +b

4000 = 300m +b

Subtract one equation from the other

1800 = 200m

m = $9/chair

This is the slope of the line and shows that it costs $9 to produce each extra chair

Now we can solve for the y intercept (b)

2200 = 100*9 +b

2200 = 900 +b

b = $1300

This means that it costs $1300 to start each day before any chairs are produced

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