a. Suppose a market research company finds that at a price of p = $6., they would sell x = 44 tiles each month. If they lower the price to p = $2, then more people would purchase the tile, and they can expect to sell x = 48 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), where you are given the values of x and p in the problem. First you need to find the slope of a line using these two points. Then with the slope and one of the points you can find the equation of the line using the point-slope method.( answer- worth 3 points - must show work).
To find the equation of the line for the demand equation, we can use the given information:
Point 1: (x1, p1) = (44, 6)
Point 2: (x2, p2) = (48, 2)
First, we need to find the slope (m) of the line using the formula:
m = (p2 - p1) / (x2 - x1)
Substituting the values:
m = (2 - 6) / (48 - 44)
m = -4 / 4
m = -1
Now that we have the slope (m), we can use the point-slope form of a line equation:
p - p1 = m(x - x1)
Substituting the values of Point 1:
p - 6 = -1(x - 44)
Simplifying:
p - 6 = -x + 44
To express p in terms of x, we isolate it:
p = -x + 44 + 6
p = -x + 50
Therefore, the equation of the demand equation line is:
p = -x + 50
This equation represents the relationship between the price (p) and the quantity demanded (x) for the tiles.