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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(13342)   (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.
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