SOLUTION: a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purc

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purc      Log On


   

Question 188040: a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).
I really need assistance with this problem. I would really appreciate any help you can offer me in solving this problem.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Take given: (x1,p1)=> (42,$20);; (x2,p2)=> (52,$10)
We get the Slope via Point Slope Form system%28m=%28p%5B2%5D-p%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29
Substituting,
m=%2810-20%29%2F%2852-42%29=-10%2F10=%28red%28-1%29%29

Thru point (42,20) via Slope-Intercept Form, y=mx+b ==> p=mx+b
20=%28-1%29%2842%29%2Bb
20=-42%2Bb ---> b=20%2B42=62, Price (Y) Intercept

*Also the same when you try point (52,10) for the Price Intercept.

It follows ==> p=-x+62, Answer
We see graph,


Thank you,
Jojo