Question 42111This question is from textbook Begining Algebra
: 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 the 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.
This question is from textbook Begining Algebra
Answer by tutorcecilia(2152)   (Show Source):
You can put this solution on YOUR website! Since this problem involves a linear equation, use the slope-intercept format:
y=mx+b
.
First, identify the x and y values along with the coordinate pairs:
Pair #1: (x, y) = (100; 10,000)
Pair #2: (x, y) = (300; 22,000)
.
Find the slope of these two points:
Slope = m = delta y/delta x = (10,000 - 22,000)/100 - 300 = 60
.
Plug in the values into the equation.
Use any (x, y) pair for the values of x and y:
y = mx + b
22,000 = (60)(300) + b
22,000 = 18000 + b
4,000 = b
Plug the value of the slope "m" and "b" into the equation:
Cost (c) = 60x + 4000
C = 60x + 4000
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