a. Suppose 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).
Use the form p = mx + b for both data points
20 = 42m + b
10 = 52m + b
Solve for m and b
10 = -10m
m = -1
20 = -42 + b
b = 62
So the equation is
p = 62 - x
or
x = 62 - p
x should be the dependent variable. p can be independently assigned.
To find the demand equation in the form p = mx + b, we can use the two points given in the problem.
The first point is (42, $20), and the second point is (52, $10).
To find the slope (m) of the line, we can use the formula:
m = (p2 - p1)/(x2 - x1)
Using the first point (42, $20) and the second point (52, $10), we have:
m = (10 - 20)/(52 - 42)
m = (-10)/10
m = -1
Now that we have the slope, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Using the point (42, $20) and the slope -1, we have:
p - 20 = -1(x - 42)
Expanding and simplifying the equation, we get:
p - 20 = -x + 42
p = -x + 42 + 20
p = -x + 62
So, the demand equation in the form p = mx + b is:
p = -x + 62