SOLUTION: 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

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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