Question 249495: 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)).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = price of the tile.
let y = number of tiles sold each month.
when x = 20, y = 42
when x = 10, y = 52
equation of a straight line in slope-intercept form is:
y = mx+b
m is the slope and b is the y intercept.
to find the slope, use the equation m = (y2-y1)/(x2-x1)
(x1,y1) = (10,52)
(x2,y2) = (20,42)
slope equals (52-42)/(10-20) = 10/-10 = -1
plug this in the general form of the equation to get:
y = -1*x + b
substitute for x and y using either of the two points used to find the equation of the line.
use (20,42)
equation becomes:
42 = -1*(20) + b
solve for b to get:
b = 62
equation of your line is:
y = -1*x + 62
graph of the equation looks like this:
|
|
|
