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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Suppose that a market place research company finds that at a price of p =$20, they would sell x=42 tiles each month. If the lower the price to p= $10,then more people would purchas      Log On


   

Question 150623: Suppose that a market place research company finds that at a price of p =$20, they would sell x=42 tiles each month. If the 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.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the demand equation (p = mx+b) if p = $20 when x = 42 and p = $10 when x = 52.
First, you can find the slope, m, of the line represented by this equation.
p is the dependent variable and x is the independent variable.
m+=+%28p%5B2%5D-p%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Make the substitutions: p%5B1%5D+=+20, p%5B2%5D+=+10, x%5B1%5D+=+42, and x%5B2%5D+=+52
m+=+%2810-20%29%2F%2852-42%29
m+=+%28-10%29%2F10
m+=+-1, so now you can write:
p+=+%28-1%29x%2Bb but now you need to find b, the p-intercept. Just substitute the p- and x-values from the given data, but make sure that you match the appropriate p with the right x (in other words, mind your p's and x's...lol).
Let's use p%5B1%5D+=+20 and x%5B1%5D+=+42
20+=+%28-1%29%2842%29%2Bb Simplify.
20+=+-42%2Bb Add 42 to both sides.
62+=+b
Now you can write your final equation:
p+=+-x%2B62
Check:
p+=+-x%2B62 Substitute x = 42.
p+=+-42%2B62
p+=+20 OK
p+=+-x%2B62 Substitute x = 52.
p+=+-52%2B62
p+=+10 OK
Here's the graph of the demand equation: (The vertical axis is p and the horizontal axis is x)
graph%28400%2C400%2C-5%2C65%2C-5%2C65%2C-x%2B62%29