Question 145992: 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. Write an equation using two points in the form (x,p)
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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. Write an equation using two points in the form (x,p)
.
The problem basically gives you two points:
p = $20 when x = 42
and
p = $10 when x = 52
.
The two points they gave you then are:
(42,20)
and
(52,10)
.
slope (given two points) is:
m = (20-10)/(42-52) = 10/(-10) = -1
.
The problem asked you to put it in the form of:
p = mx + b
plug in one (42,20) of the two given points (doesn't matter which) and the slope to solve for 'b':
20 = (-1)(42) + b
20 = -42 + b
62 = b
.
Pulling it all together we have then:
p = -x + 62
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