How do you solve this equation

Question

7000 shirts can be sold for $61.00 and 8000 shirts can be sold for $52.00, give linear equation p=mn+b, p= price, n= shirts give a price they can charge for shirts.

Answer 1

We are trying to find the the inverse demand function for shirts:

 

P = mQ + b (n is Q, or Quantity Demanded)

 

We're given 2 points (Q, P) on this line: (7000, $61) and (8000,$52)

 

First, we'll find the slope m between these points, just the change in P over the change in Q:

 

m = ($52 - $61) / (8000 - 7000) = -$9/1000, for every additional 1000 shirts available the price P buyers are willing to pay falls by $9

 

Now, with m = -$9/1000 we can use the point-slope form of a line with either one of our given points to find the equation.

 

(P - 52) = -$9/1000(Q - 8000)

P - 52 = -$9Q/1000 + $72

P = -$9Q/1000 + $124

 

So, m = -$9/1000 and b = $124