Question 202710: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups.
a. Write an equation for the number of cups you sell as a function of the price you charge.
b. Denote "C" for number of cups, and "P" for the price you charge.
c. Assume the function is linear.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Ok, let's use the "slope-intercept" form (y = mx+b) of a linear equation to develope the necessary equation, except that our "dependent variable" will be C (for number of cups) rather than y and our "independent variable" will be P (for price) rather than x.
So we can start with:
 where m is the slope of the line and b is the y-intercept.
The problem gives us two points to start us off.
P = $2 & C = 120 cups. We can write this as an ordered pair (2, 120)
P = $3 & C = 60 cups. We can write as an ordered pair (3, 60)
Now we have two points that will satisfy our equation, we can calculate the slope, m, from the formula for the slope.
 but, instead of using x and y, we want to use P and C respectively, so...
 Substitute:  ,  ,  , and 
 Evaluate.
 So now we have...
 Next, we need to find the value of b, the y-intercept (or, in this problem, the C-intercept). This is done by substituting the C- and P-values from either one of the two given points that we started off with.
Let' use (2, 120).
 Add 120 to both sides.
 or 
Ok, we can now write the final equation:
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