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

p = -0.006n + 102

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