Suppose a market research company finds that at a price of p=$25,they would sell x=56 tiles each month. If they lower the price to p=$20, then more people would purchase the tile, and they can expect to sell x=66 tiles in a month's time. Find the equation of the line for the demand equation. Writ answer in the form p=mx+b
for this problem, we will substitute the given to the equation p = mx + b, and then we solve simultaneously (two equations, two unknowns):
25 = 56m + b
20 = 66m + b
to solve this, we can multiply one equation by -1 so that if we add the equations, the b will be cancelled:
-25 = -56m - b
20 = 66m + b
-----------------------
-5 = 10m
m = -1/2
to get be, we substitute this m to either equations. In this case, let's just substitute to the first equation:
25 = 56m + b
25 = 56(-1/2) + b
25 = -28 + b
b = 53
therefore, the equation is
p = (-1/2)x + 53
hope this helps~ :)