Question

A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 5000 shirts can be sold at a price of $ 72 , while 10000 shirts can be sold at a price of $ 42 . Give a linear equation in the form p = m n + b that gives the price p they can charge for n shirts.
P=________________________

Answer 1

Answer:

p = -0.006n + 102

Step-by-step explanation:

So you have two data points and you want to find line between them in y-intercept form

    5000 shirts can be sold at a price of $ 72  

   10000 shirts can be sold at a price of $ 42

    p = m n + b               y = mx + b     y = price of shirts  x = number of shirts

   m = (p2 - p1) / (n2 - n1)            (5000, 72) and (10000, 42)

       = (72 - 42) / (5000 - 10000)

       =    30 / -5000

       =    - 0.006

   p = -0.006n + b

   p - 72  = -0.006(n - 5000)

   p = -0.006n - (0.006)(-5000) +72

      = -0.006n + 30 + 72

  p = -0.006n + 102