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Question 179121: 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 MissionPossible(18)   (Show Source):
You can put this solution on YOUR website! p = 20 , x = 42
because p = mx + b
then
20 = m(42) + b ----------(1)
p = 10 , x = 52
then
10 = m(52) + b -----------(2)
2 equation with 2 variables
you can do many ways to solve it.
First way of solution:
Equation minus equation in each side
In the left side 20-10 = 10
in the right sied (m(42) + b)-(m(52) + b) = (-10)m
then 10 = (-10)m
m = -1
at the equation(1) put (-1) instead of m
20 = (-1)(42) + b
20 = -42 + b
20 + 42 = b
b = 62
Then answer in the form p = mx + b is
p = (-1)x + 62
The Second way of solution:
p = 20 , x = 42
because p = mx + b
then
20 = m(42) + b ----------(1)
p = 10 , x = 52
then
10 = m(52) + b -----------(2)
From equation(1) b = 20 - 42m put this (20-42m) instead of b in the equation(2)
10 = m(52) + (20-42m)
10 = 10m + 20
-10 = 10m
m = (-1)
Put this (-1) instead of m in the equation(2)
10 = (-52) + b
10 + 52 = b
b = 62
Then answer in the form p = mx + b is
p = (-1)x + 62 (The same as the first solution)
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