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).

Question

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).

Answer 1

To find the equation of the line for the demand equation, we need to determine the slope (m) and the y-intercept (b) using the given points (x, p).

Using the two given points:
(42, 20) and (52, 10)

First, we can calculate the slope (m) using the formula:
m = (p2 - p1) / (x2 - x1)

Substituting the values:
m = (10 - 20) / (52 - 42)
m = -10 / 10
m = -1

Now that we have the slope (m), we can use it to find the y-intercept (b) using one of the points.
Using (42, 20):

p = mx + b
20 = -1 * 42 + b
20 = -42 + b

To solve for b, we add 42 to both sides:
20 + 42 = b
62 = b

Thus, the equation of the line for the demand equation is:
p = -x + 62

So, the demand equation can be written as p = -x + 62.