6.5 million/lb of coffee are sold at $8/lb and 4.0m lb are sold when it is $9/lb?

Question

(a)Find a linear function that expresses the amount of coffee sold as a function of the price per pound.

(b)Use the function of part (a) to predict how much consumers would be willing to buy at a price of $6/lb.

so far I came up with (6.5 - 4) divided by (8-9).... which then I came up with the equation... y-9= -2.5x - 20...or y= 2.5x - 29.... is this right so far? how do i do part b?

what is the domain?

Answer 1

consider 6.5 million lb of coffee are sold at $8/lb and 4.0m lb are sold when it is $9/lb as 2 points (8;6.5) and (9;4.0).
We can make a linear function by setting:
(6.5 - 4.0) = m * (9 - 8)
so m = 2.5
then we have y - 6.5 = 2.5 * (x - 8)
thus the function is y = 2.5*x +4.5

consider $6/lb as x in the above function y = 2.5*x +4.5
Find y, then u will know how much consumers would be willing to buy. Do it by yr self.
my result is 19.5m lb
COMMENDATION: u see that when the price of coffee decrease the number of consumers increase and conversely. thus yr curve of this function is downward sloping.

Answer 2

the answer is really quite simple despite the errors made above.

6.5 million lb of coffee are sold at $8/lb and 4.0m lb are sold when it is $9/lb as 2 points (8;6.5) and (9;4.0).

We can make a linear function by setting:
(6.5 - 4.0) = m * (9 - 8)
so m = 2.5
y - 6.5 = 2.5 * (x - 8)
y = 2.5*x +4.5

Regard $6/lb as x in the above function y = 2.5*x +4.5

Find y, then you will know how much consumers would be willing to buy. Do it by yourself. The correct result, without errors in the calcuation is 19.5m lb

You see that when the price of coffee decreases the number of consumers increase, and conversely. So your curve of this function slopes downward.