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Question 565987: I have to create a demand equation. My problem is to 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.
I know my answer needs to be written in the form p=mx+b and I know my equation needs two points in the form (x,p). I know I need to plug in my information from the above problem using the x values of $10 and $20 and I need to use my tiles of 42 and 52, but I cannot figure out how to structure the problem showing all my work.
Thank you for your help.
Lindsay
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! I have to create a demand equation. My problem is to 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.
I know my answer needs to be written in the form p=mx+b and I know my equation needs two points in the form (x,p). I know I need to plug in my information from the above problem using the x values of $10 and $20 and I need to use my tiles of 42 and 52, but I cannot figure out how to structure the problem showing all my work.
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The equation is of the form p = mx + b
We can use the given information to obtain 2 equations in 2 unknowns:
Given: p=20 when x=42 20 = 42m + b
Given: p=10 when x=52 10 = 52m + b
Subtract the 2nd equation from the 1st:
10 = -10m
m = -1
Now substitute this value into one of the two equations above
10 = -52 + b -> b = 62
So the equation is p = -x + 62
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