Expert: Paul Klarreich - 1/8/2008

Question
a.   Suppose that 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
Questioner:   amanda
Category:  Advanced Math
Private:  No
 
Subject:  demand equations
Question:  a. Suppose that 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))
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Hi, Amanda,

If that's all you need, then your two points are (42,20) and (52,10)

Subst into  p = mx + b:

42 = m(20) + b
52 = m(10) + b

42 = 20m + b
52 = 10m + b

Solve for m and b (simultaneous equations)

10m = -10,

m = -1

52 = -10 + b

b = 62.

Your equation is  p = -x + 62.