SOLUTION: 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. Projectio

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Question 85817: 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 tutorcecilia(2144) About Me  (Show Source):
You can put this solution on YOUR website!
First, find and identify the x's and the y's:
x=100 items
y=$10,000
.
and x=300 items
y=$22,000
.
Next, use the formula for the slope (m) of a line:
Slope = m = %28%28y1-y2%29%2F%28x1-x2%29%29 [plug-in the values and solve for the slope]
Slope = m = %2822000-10000%29%2F%28300-100%29%29 = 60
.
Now, use the formula for the slope-intercept formula:
y=mx+b [plug-in the values and solve for the b-term]
22,000=(60)(300)+b
22,000=18,000+b
22,000-18,000=b
4,000=b
.
y=60x+4000 [plug-in the values of the slope and the y-intercept (b) for the equation of the line]
.
checking:
y=60x+4000 [pick a point and plug it into the equation]
10,000=(60)(100)+4000
10,000=10,000 [checks out]