Question

a. Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p).

Answer 1

if we know that when p =$20, x=42 we can find:
p = mx + b
20 = m(41) + b (1)

and from p=$10 when x=52, we can find:
p = mx + b
10 = m(52) + b (2)


use eqt. (1) to find b:
b = 20 - 42(m)

apply b into eqt. (2):
10 = 52(m) + 20 - 42(m)
52(m) - 42(m) = 10 - 20
10(m) = -10
[ m = -1 ] ans.

with m, form the eqt.:
p = -x + b (3)

plug either points (42,20) or (52,10) to find b:

20 = -42 + b
b = 62

10 = -52 + b
b = 62


hence,

p = -x + 62


is that right?