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Question 342264: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 48 cups. But when you raise your price to $2 you only sell 27 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 MathTherapy(10549)   (Show Source):
You can put this solution on YOUR website! Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 48 cups. But when you raise your price to $2 you only sell 27 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.
Since the number of cups sold is dependent on the price charged, we will use the cost per cup as the independent or x variable and the amount of cups sold as the dependent or y variable.
From the information given, we will have two coordinate points: (1, 48) & (2, 27). We will use these points to determine the slope of the linear equation, or m.
Using the slope-intercept form,  , one of the points, (1, 48) and the slope, - 21, we can then determine the linear equation, as follows:
y - 48 = - 21(x - 1)______y - 48 = - 21x + 21_____y = - 21x + 69
Now, for the amount of cups sold, we can substitute C(P) for y, and for the price charged, per cup, we can substitute P for x to get the equation for the number of cups sold as a function of the price charged: 
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