Afriend tells ben that she buys her oil from cheap oil. when she bought 600 litres the price was $620. another time she bought 540 litres for $566.
a. what is the equation that represents the total cost of buying oil from cheap oil?
b. what is the delivery charge for cheap oil?
c. if ben needs 650 litres of oil which company should he pick? justify your answer with appropriate math.

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.

Lines that intersect at one point