a. Suppose that a market research company finds that at a price of p = $40, they would sell x = 37 tiles each month. If they lower the price to p = $25, 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)).
1. Suppose a market research company finds that at a price of p = $35, they would sell x = 50 tiles each month. If they lower the price to p = $25, then more people would purchase the tile, and they can expect to sell x = 70 tiles in a month’s time. Find the equation of the line for the demand equation. Hint: Write your answer in the form p = mx + b.
a. Suppose a market research company finds that at a price of p = $40, they would sell x = 27 tiles each month. If they lower the price to p = $15, then more people would purchase the tile, and they can expect to sell x = 47 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).
To find the equation of the line for the demand equation, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
In this case, we want to find the equation in terms of price (p) and quantity demanded (x). Let's use the two given points: (37, 40) and (52, 25).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (25 - 40) / (52 - 37)
m = -15 / 15
m = -1
Now, let's substitute the slope (m) into the equation:
p = mx + b
p = -1x + b
Next, let's substitute one of the given points into the equation to find the y-intercept (b). Let's use the point (37, 40):
40 = -1(37) + b
40 = -37 + b
b = 77
Now, substitute the value of the y-intercept (b) into the equation:
p = -1x + 77
Therefore, the equation of the line for the demand equation is:
p = -x + 77