SOLUTION: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for

Algebra ->  Graphs -> SOLUTION: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for      Log On


   

Question 121745: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).

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 by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to use "y" instead of "p"

Since the price is p=$20, this means y=20 when x=42. So we have the first point (42,20).


Also since the price is p=$10, this means y=10 when x=52. So we have the second point (10,52).

So let's find the equation of the line through the points (42,20) and (10,52):

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First lets find the slope through the points (42,20) and (10,52)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (42,20) and is the second point (10,52))

m=%2852-20%29%2F%2810-42%29 Plug in y%5B2%5D=52,y%5B1%5D=20,x%5B2%5D=10,x%5B1%5D=42 (these are the coordinates of given points)

m=+32%2F-32 Subtract the terms in the numerator 52-20 to get 32. Subtract the terms in the denominator 10-42 to get -32


m=-1 Reduce

So the slope is
m=-1

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-20=%28-1%29%28x-42%29 Plug in m=-1, x%5B1%5D=42, and y%5B1%5D=20 (these values are given)


y-20=-x%2B%28-1%29%28-42%29 Distribute -1

y-20=-x%2B42 Multiply -1 and -42 to get 42

y=-x%2B42%2B20 Add 20 to both sides to isolate y

y=-x%2B62 Combine like terms 42 and 20 to get 62



So the equation of the line which goes through the points (42,20) and (10,52) is:y=-x%2B62

p=-x%2B62 Now replace y with p

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Answer:

So the demand equation is:
p=-x%2B62