Question 6936: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $2 you only sell 30 cups. Write an equation for the number 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 by glabow(165)   (Show Source):
You can put this solution on YOUR website! When P=1 then C=60.
When P=2 then C=30.
If you assume the function of P to C is linear, then you can calculate the change in C compared to the change in P.
This is called the slope of the line of an equation fitting these values.
 is the slope.
This means that every time you increase P by 1, C will decrease by 30. That's the nature of a linear function.
The function of a line is y = ax + b, where a is the slope and b is the value of y when x=0 (called the y-intercept). In this case we are using C for y and P for x. The equation of the line is
C = -30P + b.
If the P were 0, what would C be? The slope tells us that every time you increase P by 1, C decreases by 30. Inversely, every time you decrease P by 1, C increases by 30. So when P=0, C=90.
The equation is
C = -30P + 90. (Not very realistic, but this fits the requirements of the problem.)
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