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

20 = m*42 + b

10 = m*52 + b

10 = -10m
m = -1
20 = -42 + b
b = 62

p = -x + 62

Answer 2

Thanks drwls

Answer 3

To find the equation of the demand line, we need to determine the slope and the y-intercept of the line.

Given the points (x1, p1) = (42, 20) and (x2, p2) = (52, 10), we can use the formula for the slope of a line:

slope (m) = (p2 - p1) / (x2 - x1)

Substituting the values:

slope (m) = (10 - 20) / (52 - 42) = -10 / 10 = -1

Now that we have the slope (m), we can use the point-slope form of a linear equation to find the equation of the line:

p - p1 = m(x - x1)

Using the point (x1, p1) = (42, 20):

p - 20 = -1(x - 42)

Simplifying:

p - 20 = -x + 42

Finally, rearranging the equation to the form p = mx + b, where b represents the y-intercept:

p = -x + 42 + 20

p = -x + 62

Therefore, the equation of the demand line is p = -x + 62.