Expert: Paul Klarreich - 6/15/2008

Question
I am having trouble coming up with the proper equation for the following:  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:   Vickie
Category:  Advanced Math
Private:  No
 
Subject:  Polynomial word problems
Question:  I am having trouble coming up with the proper equation for the following:  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, Vickie,

Your last sentence, the 'hint' says it all:

Write an equation using two points in the form (x,p)).
You have:

 x1 = 42, p1 = 20.
 x2 = 52, p2 = 10.

Now you want the equation of a line. For this, use the 'two-point' form:

p - p1    p2 - p1
------- = --------
x - x1    x2 - x1

Plug it in, Plug it in, as that commercial says:

p - 20    10 - 20
------- = --------
x - 42    52 - 42

Do some simplifying:

p - 20    - 10
------- = -----
x - 42      10


p - 20    - 1
------- = -----
x - 42      1

p - 20 = - x + 42

p = -x + 62