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Question 242465: My problem is regarding "demand equation" or demand curve. Here is the word problem:
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 months time. Find the equation of the line for the demand equation. Write your answer in the form p=mx+b. (Hint:Write and equation using tow points in the form (x,p)).
I understand that this involves the slope formula y=mx+b. I just do not know where to go from there.I do not know how to get the numbers for m and b. If anyone could help me to get started, that would be great.
If possible, please provide a step by step solution, so that I may use it for a study guide.
Thank you.
Found 2 solutions by MRperkins, solver91311:
Answer by MRperkins(300)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Let's begin with a point of terminology usage.  is NOT "the slope formula." It is the slope-intercept form of the equation of a line.
The next thing you need to realize is that there are four basic forms of the equation of a line.
There is the two-point form used to derive an equation of the line when you are given the coordinates of two points. It looks like this:
(x\ -\ x_1) )
Where ) and ) are the coordinates of the given points.
There is the point-slope form used to derive an equation of the line when you are given (or can otherwise easily determine) the slope and you are given the coordinates of a point on the line. It looks like this:
)
Where  is the slope and are the coordinates of the given point.
There is the slope-intercept form used to derive an equation of the line when you are given (or can otherwise easily determine) the slope and you are given the coordinates of a particular point on the line, that point being the  -intercept, ) . It looks like this:
Where is the slope and are the coordinates of the intercept.
Lastly, there is standard form which is generally used to represent a line in a system of linear equations. It looks like this:
Some texts require that A, B, and C be integers in order to be correctly in standard form.
Any of the forms can be manipulated into any of the other forms. The decision on which to use is based solely on what you know when you start the problem.
In your case, you are given two different price points,  , $20 and $10, and two different quantity sold amounts,  , that correspond to the price points, namely 42 and 52. You are given a hint to use points of the form ) , so just form the points:
)
)
Since you are given two points, the logical thing to do, from my point of view, is to use the two-point form of the equation of a line and substitute the above coordinate values: (Remember to replace with )
(x\ -\ x_1))
(x\ -\ 20))
Performing the indicated arithmetic and rearranging the above equation is left as an exercise for the student. Remember you want to end up with the slope-intercept form: 
One of the things that this problem will illustrate for you once you have determined that the intercepts are (62,0) and (0,62) is the limitations of a linear model for a real world situation. The linear model given will insist that if you set the price at $0 you will sell exactly 62 and if you pay people $10 each, you will sell exactly 72. If you set the price at $72, people will be bringing tiles back to your store. The model may be a good representation when you are charging between $10 and $40 per tile, but falls apart when either the price or the number sold gets close to or goes beyond 0
John
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