Question

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.

Answer 1

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 :)