Question 999698: A company that makes nails finds that it would sell 42 boxes of nails per month if they are priced at $20 per box. If the company lowers the price to $10 per box, then more people would purchase nails and the company could expect to sell 52 boxes per month. Find the equation of the line for the demand equation if x represents the number of boxes sold and y is the price of a box of nails.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! at 20 dollars a box, 42 boxes are sold per month.
at 10 dollars a box, 52 boxes are sold per mmnth.
your demand equation is y = mx + b
y is the price per box.
x is the demand.
m is the slope
b is the y-intercept
there are 2 points on your demand line.
they are (x1,y1) = (42,20) and (x2,y2) = (52,10).
m = slope = (y2-y1) / (x2-x1) = (10-20)/(52-42) = -10/10 = -1
y = mx + b becomes:
y = -1*x + b which becomes:
y = -x + b
to find b, replace x and y with the coordinates of one of the points on the line and solve.
we'll use (42,20)
y = -x + b becomes:
20 = -(42) + b
add 42 to both sides to get:
62 = b
equation becomes:
y = -x + 62
that's your demand equation.
when x = 0, y = 62
when x = 42, y = 20
when x = 52, y = 0
etc.
the graph of this equation looks like this:
actually i would call this the price equation because your x value is the demand and your y value is the price.
since y is dependent on the value of x, that means that price is dependent on the value of the demand.
you would normally use this equation to find the price given the demand.
a true demand equation would have x = price and y = demand.
you would use that equation to find the demand given the price.
but, the problem stated x = demand and y = price so that's what i created the equation for.
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