Question 380854: When soft drinks sold for $0.80 per can at football games, approximately 6500 cans were sold. When the price was raised to $1.00 a can, the demand dropped to 4000. Assume that the relationship between the price p and the demand y is linear.
Write a linear function giving the demand y as a function of p.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let y = number of cans sold.
let x = price per can.
when x = .8, y = 6500
when x = 1, y = 4000
you have 2 points from which you can generate a linear equation.
the point slope form of the linear equation is y = mx + b.
m is the slope and b is the y intercept.
the general form of the slope of the line is (y2-y1)/(x2-x1)
you have 2 points.
they are:
(.8,6500) and (1,4000)
x1 = .8
y1 = 6500
x2 = 1
y2 = 4000
your slope is (y2-y1)/(x2-x1) which becomes (4000-6500) / (1-.8).
this becomes -2500 / .2 which becomes -12500.
that's your slope and the slope intercept form of your equation becomes:
y = -12500*x + b
to find the y intercept, substitute one of the points for y and x.
we'll use (.8,6500)
the equation becomes:
6500 = -12500*(.8) + b
that becomes 6500 = -10000 + b
solve for b to get b = 16500
your equation becomes:
y = -12500*x + 16500
when x = .8, y becomes 6500
when x = 1, y becomes 4000
The slope is -12500
the y intercept is 16500
the equation is y = -12500*x + 16500
graph this equation and it looks like this:
when x = 0, y = 16500
when x = .8, y = 6500
when x = 1, y = 4000
It's hard to see from the graph, but if you plot real careful the intersection of x = 1 and y = 4000, you will see that they intersect on the line of y = -12500*x + 16500.
The more exact way is to simply solve the equation of y = -12500*x + 16500 when x = .8
you get y = -12500*(.8) + 16500 which becomes y = -10000 + 16500 which becomes y = 6500.
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