Question 169154: Good Morning, I really need help with this problem: I am unsure of where to even begin. I am taking this class online and am finding my professor be less than helpful. So here it is.
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 nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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)).
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Your "profit" formula is:
P(x)
.
The two (x,p) points they give you are:
(x,p) = (52,10)
(x,p) = (42,20)
.
The "form" they want it in is:
p = mx + b
where
p is the profit
m is slope
x is the tiles sold
b is the "y-intercept"
.
To find 'm', the slope (given two points):
m = (p2-p1)/(x2-x1)
plugging in your points:
m = (20-10)/(42-52)
m = 10/-10
m = -1
.
Now, using any one of the points (let's use 42,20) and the slope plug it back into (to find 'b'):
p = mx + b
20 = (-1)(42) + b
20 = -42 + b
62 = b
.
Recapping, we have:
m = -1
b = 62
.
To complete, insert the above into:
p = mx + b
p = (-1)x + (62)
p = -x + 62 (This is what they're looking for)
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