SOLUTION: 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 t

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: 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 t      Log On

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 261713: 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 months'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). My biggest problem is I am not sure about the demand equation, I am not real clear on what I am suppose to be figuring out in this problem. I have several other problems which depend on my having this base correct. I am totally blank and have read everything I have on this and I must be over looking or thinking this out. Please help me. Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!They are asking you to write your answer in the form p = m*x + b. If I take that literally, then at a price of 20, the equation would become: 20 = m*x + b this kind of says that the price per tile is a function of the number of tiles sold per month which doesn't make a hell of a lot of sense, because it usually is that the number of tiles sold per month is a function of the price per tile. I would think the formula should be: 42 = m*x + b where x is the cost per tile. you would then get: 42 = m*20 + b, and you would also get: 52 = m*10 + b. now the number of tiles sold per month is dependent on the price per tile which I believe is what you are looking for. I can see why you are confused. I am too. If you are looking at a demand equation, then you want to find the demand based on the price. I will assume my interpretation is correct and work it that way and see where it goes. let's assume, the equation is: d = m*p + b this means demand = slope of the line times the price per unit + b, where b is the demand if the price is 0. That doesn't make a hell of a lot of sense, but these straight line equations are usually only valid in a limited range of the domain so we can use it even if there are logical consistencies involved at the extremes. our equation is: d = m*p + b our coordinate points are: (p1,d1) = (20,42) (p2,d2) = (10,52) we find the slope (m) by the formula (d2-d1)/(p2-p1) = (52-42)/(10-20) = 10/-10 = -1. our equation becomes: d = -1*p + b we substitute one of the points on the line to find b. take (p2,d2) = (10,52) equation becomes: 52 = -1*10 + b which becomes 52 = -10 + b which becomes 62 = b after you add 10 to both sides of that equation. our equation becomes: d = -p + 62 when p = 0, then d = 62 when p = 10, then d = 52 when p = 20, then d = 42 we let y = d and x = p so we can graph this equation. equation becomes: y = -x + 62 graph of the equation is shown below: this is your demand equation. it is estimating the demand based on the price. y values are the demand. x values are the price. as the price goes up, the demand goes down. as the price goes down, the demand goes up. they threw you a curve when they said use the equation in the form of p = m*x+b and when they showed you that p = 20. this means that p is the price per unit and the equation is not a demand equation but a price equation which is making the price dependent on the demand rather than the demand dependent on the price. I think that what you are looking for is the demand equation which means that the demand is dependent on the price, so the equation I gave you is accurate. If the price were dependent on the demand, then that would be a price equation which is not what I think you are looking for.