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Question 471138: Suppose 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 Theo(13342)   (Show Source):
You can put this solution on YOUR website! slope intercept form of the equation of a straight line is:
y = mx + b
m is the slope
b is the y intercept
the slope is equal to (y2-y1) / (x2-x1)
x is the price per tile
y is the demand
x1 = 20
y1 = 42
x2 = 10
y2 = 52
m = (y2-y1) / (x2-x1) = 10 / -10 = -1
slope intercept form of the equation becomes:
y = -x + b because m = -1
point slope form of the equation for a straight line is:
y-y1 = m * (x-x1)
take any of the points and substitute for x1 and y1 to get:
we'll use (x1,y1) = (20,42)
we get:
y - 42 = -1 * (x-20)
this becomes:
y - 42 = -x + 20
add 42 to both sides of the equation to get:
y = -x + 62
our slope is -1 and our y intercept is 62
our equation is:
y = -x + 62
a graph of this equation is shown below:
I drew 2 horizontal lines at y = 52 and y = 42 so you can better see that, when y = 52, x = 10, and when y = 42, x = 20.
x is the price per tile.
y is the demand in number of tiles.
just drop a vertical line from the intersection of those 2 horizontal lines with the line of the equation to see the value of x.
it will be in the area of x = 10, and x = 20.
plugging x = 10 and x = 20 in the equation gets you the exact value of y.
alternatively, plugging y = 52 and y = 42 in the equation gets you the exact value of x.
for example:
the equation is y = -x + 62
when y = 52, this equation becomes 52 = -x + 62
add x to both sides of the equation and subtract 52 from both sides of this equation gets you x = 10.
this graph is showing the demand per month (y) based on the price per tile (x).
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