We have two points on the graph that describes the cost of oil from Cheap
Oil. We can use these two points to write the equation of a straight line.
We don't know for sure that the cost of the company's oil actually follows
that line, but that's the best we can do with the information we have.
The two points we have are:
Quantity = 600 Cost = 620 (600, 620)
Quantity = 540 Cost = 566 (540, 566)
The slope of the line is (620 - 566) / (600 - 540) = 54/60 = 0.9
The equation of the line is C = 0.9Q + intercept
To find the intercept, plug point #1 into the equation:
620 = (0.9) (600) + intercept
620 = (540) + intercept
Subtract 540 from each side: 80 = intercept
So the linear equation for the straight-line through these two points is
a). Cost = 0.9 (Quantity) + 80 dollars.
b). The $80 is a cost that's stacked on to every order, on top of the
quantity cost. We don't know what that $80 really pays for; it's just
an additional cost to actually get your oil. That's the amount that the
problem calls the "delivery charge" ... an appropriate label perhaps,
in view of the fact that even after you've paid in full for the amount of
oil you bought, youse still ain't gettin anything delivered until youse
coughs up another 80 bucks for the driver's retirement account.
c). If Ben needs 650 liters of oil, we don't know of any other place for him
to buy it besides Cheap Oil. There may have been some discussion of
another supplier and their pricing before we came along, but we were not
present, so we can't advise Ben.
