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Question 80886: This is my question:
You own a lemonade stand, when you charge $2 a cup you sell 120 cups. When you raise the price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. "c" for number of cups and "p" for the price charged. Assume the function is linear.
I have been working on this for days and can't figure it out. Please help!
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! I would start with the slope-intercept form of a linear equation:
y = mx + b
But, because you are addressing variables that are different from x (the independent variable) and y (the dependent variable), I would change to the variables P (the independent variable) and C (the dependent variable).
In this problem, C (the number of cups sold) is the dependent variable because it depends on the price (P) that is charged for each cup.
Since you are given two ponts (P, C) on the line: (2, 120) and (3, 60) you can find the slope, m by using the slope formula:  or, in your variables:
So you can write:
C = -60P + b Remember, we are substituting C for y and P for x.
Now you need to find the value of b, the y-...oops, I mean the C-intercept.
You can do this by substituting the C and P values from one of the given points, say (3, 60) into this equation and solve for b.
60 = -60(3) + b Simplify.
60 = -180 + b Add 180 to both sides.
240 = b
Now you can write the final equation:
C = -60P + 240
Check:
For P = $2 and C = 120 cups:
120 = -60(2)+240
120 = -120+240
120 = 120
...and for P = $3 and C = 60 cups:
60 = -60(3)+240
60 = -180+240
60 = 60
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