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Question 64972: I have tried and tried to remember the formulas and have done research to refresh my memory, but it's just not working. Here's the question:
If you charge $1 per cup of a drink and sell 50 cups, then you raise your price to $2 per cup and sell only 25 cups, write an equation for the number of cups that you sell as a function of the price you charge. "C" is for # of cups and "P" is for the price you charge. Assume that the function is linear.
Thank you
This problem is from an assignment from a course through correspondence.
Answer by cristiana(10)   (Show Source):
You can put this solution on YOUR website! All right, so the start point is that our function is linear.
Draw the coordinate system.
Let the price be x and number of cups be y.
We know that when x = 1, y = 50. Plot this point.
We also know that when x = 2, y = 25. Plot this point too.
Draw a line between the two plotted points.
Let's try to find the point-intercept equation of this line. Since all we know is the two points, we can make a system of two point-slope equations and find the slope. Let's do that:
point (1,50): y-50 = m(x-1); y = m(x-1) + 50
point (2,25): y-25 = m(x-2); y = m(x-2) + 25
Therefore, m = -25
Substitute -25 for m in any of the above two equations to get:
y=-25(x-1)+50
or
y=-25(x-2)+25
You can now check these equations by replacing x=1 ($1/cup) and x=2 ($2/cup)...
Hope it helped!
Cristiana
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