SOLUTION: You are selling cups of coffee at a sporting event. Your sales records show that when the coffee is priced at $3 per cup, you sell 650 cups. When the coffee is prices at $2.50, you

Algebra ->  Graphs -> SOLUTION: You are selling cups of coffee at a sporting event. Your sales records show that when the coffee is priced at $3 per cup, you sell 650 cups. When the coffee is prices at $2.50, you      Log On


   

Question 316017: You are selling cups of coffee at a sporting event. Your sales records show that when the coffee is priced at $3 per cup, you sell 650 cups. When the coffee is prices at $2.50, you sell 930 cups.
Using that information, write a linear equation for the relationship between price (p) and quantity (q) sold. Your starting point is: q = mx + b, which is the slope intercept form of an equation, and using the two ordered pairs you find m and b. Make sure your answer here is an equation.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Basically, we're looking for the equation that goes through the points and


First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=3 and y%5B1%5D=650.
Also, is the second point . So this means that x%5B2%5D=2.5 and y%5B2%5D=930.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28930-650%29%2F%282.5-3%29 Plug in y%5B2%5D=930, y%5B1%5D=650, x%5B2%5D=2.5, and x%5B1%5D=3


m=%28280%29%2F%282.5-3%29 Subtract 650 from 930 to get 280


m=%28280%29%2F%28-0.5%29 Subtract 3 from 2.5 to get -0.5


m=-560 Divide


So the slope of the line that goes through the points and is m=-560



Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-650=-560%28x-3%29 Plug in m=-560, x%5B1%5D=3, and y%5B1%5D=650


y-650=-560x-560%28-3%29 Distribute


y-650=-560x%2B1680 Multiply


y=-560x%2B1680%2B650 Add 650 to both sides.


y=-560x%2B2330 Combine like terms.


So the equation that goes through the points and is y=-560x%2B2330


Now simply replace 'x' and 'y' with 'p' and 'q' to get q=-560p%2B2330