SOLUTION: A research market 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 c

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A research market 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 c      Log On


   

Question 548279: A research market 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 I need the equation of the line for the demand equation and then a answer using the form p=mx+b . I have to write an equation using two points in the form (x,p)
Answer by Sarpi(32) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of a straight line is y = mx + c and the answer needs to be in the form p = mx + c. so y=p
if x = 42 then p = 20 and
if x = 52 then p = 10
However, we find the slope or 'change' in these figures in order to write a linear equation.
slope m = %28Y2-Y1%29%2F%28X2-X1%29 ; X1= 42, X2= 52, P1= 20 and P2= 10
m = %2810-20%29%2F%2852-42%29
m = -10%2F10 therefore the slope = -1
The equation is p = mx+c where m=slope,and c =constant.
We solve for c given x= 42, p = 20 (or can choose the other pair) and m= -1
p = mx + c
20 = -1*42 + c
20 = -42 + c
20+42 = c
therefore c = 62
Hence the demand equation giving the price (p) in terms of quantity (x) is
p = -x + 62