SOLUTION: 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

Question 121745: 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 jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm going to use "y" instead of "p"

Since the price is p=$20, this means y=20 when x=42. So we have the first point (42,20).

Also since the price is p=$10, this means y=10 when x=52. So we have the second point (10,52).

So let's find the equation of the line through the points (42,20) and (10,52):

---------------------

First lets find the slope through the points (,) and (,)

Start with the slope formula (note:

is the first point (,) and

is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

------------------------------------------------

Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and

is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add to both sides to isolate y

Combine like terms and to get

So the equation of the line which goes through the points (,) and (,) is:

Now replace y with p

---------------------------------------------------------------
Answer:

So the demand equation is:

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