Posted by Stephanie on Monday, January 19, 2009 at 11:36am.
Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cupes. But when you raise your price to $2 you only sell 25 cups. Write an equation for the nuber of cups you sell as a function of the price you charge. Denote "C" for number of cups and "p" for the price you charge. Assume the function is linear.

Math  Damon, Monday, January 19, 2009 at 12:43pm
c = m p + b
50 = m (1) + b
25 = m(2) + b
 subtract
25 =  m
m = 25 the slope
then
25 = 25 (2) + b
75 = b the intercept with cup axis
so
c = 25 p + 75
so if I charged nothing, I would give away 75 cups
and if I charged three, I would sell none :)
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