A company discovers that to produce x860 new electronic part

A company discovers that to produce x=860 new electronic parts, it will cost y=$71840. To produce 700 new electronic parts, it will cost $59200.

Compute the slope of the costs and choose the most accurate statement from the following:

-Costs are increasing at a rate of $83 per item.

-Costs are decreasing at a rate of $77 per item.

-Costs are increasing at a rate of $79 per item.

-Costs are decreasing at a rate of $79 per item.

-Costs are increasing at a rate of $77 per item.

-Costs are decreasing at a rate of $83 per item.

Solution

Let the increase in cost be y corresponding to the number of new parts x. Then the cost line passes through the points ( 860, 71840) and ( 700, 59200). The slope of cost line is (71840 - 59200)/ ( 860 - 700) = 12640/160 = 79. The slope being (positive) 79., the correct statement is that the costs are increasing at a rate of $ 79 per item. The 3rd option is correct.

Note: The slope of a line passing through the points ( x₁ , y₁) and ( x₂, y₂) is ( y₂ - y₁)/(x₂ - x₁).