Question 172453: 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 stanbon(75887)   (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. (Hint: Write an equation using two points in the form (x,p)).
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You have two points: (42,20) and (52,10)
slope = (10-20)/(52-42) = -1
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intercept: p = mx + b; solve for "b" as follows:
20 = -2(42) + b
b = 20 + 84
b = 104
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EQUATION:
p = -x + 104
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Cheers,
Stan H.
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