SOLUTION: I sent this one before but I have not received a response. Please help. Business and finance. In planning for a new item, a manufacturer assumes that the number of items produced

Question 73868: I sent this one before but I have not received a response. Please help.
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 jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you were to plot these points, you would plot them on a graph where x is the number of items produced and y is the cost. If you found the slope of the line between the 2 points, you could find the equation. So lets find the slope:

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

------------------------------------------------

Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

------------------------------------------------------------------------------------------------------------

Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.

In other words, the rate of change of the cost to the number of items is $60 per unit. Now use the point-slope formula to find the equation
Plug in m=60 and

to the equation

So this is your equation. If you plug in x=100 units, you should get y=$10,000 and if you plug in x=300, you should get y=$22,000 (y is the cost)

Check:

Works

Works
Hope this makes sense.

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