Question 156992: I need a demand equation for the following: 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, 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 an equation using two points in the form (x,p)
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i'm not totally sure what they want, but it appears they want the y value to be the number of units sold per month and the x value to be the price.
making that assumption, i get the following:
x = 20, y = 42
x = 10, y = 52
when x drops 10 units, y increases 10 units.
the slope of the line is the change in y divided by the change in x.
the slope is -1 (+10 for y / -10 for x)
so the partial formula is y = -1x.
to complete the equation, we need to fix y for one of the known points.
take x = 20.
at that point y = 42.
from the formula y = -x, y = -20 when x = 20.
to get to 42, we need to add 62.
the formula becomes y = -x + 62.
now when x = 20, y = 42.
to test the formula for the other known point, we take x = 10.
when x = 10, y = -10 + 62 = 52.
that's where we want to be so the formula is good.
formula you are looking for is y = -x + 62.
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