Suppose that a market research company finds that at a price of p = $30, they would sell x = 36 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 = 41 tiles in a month’s time.

Write two ordered pairs in the form (x, p) that represent the market research. (1 pt)
Find the equation of the line for the demand equation using the two points in #1. Write your answer in the form P=mx+b. (Show all of your work) Hint: 1st, Find slope (m) using the two ordered pairs you created. Replace both x variables and both y variables in the formula (p-p_1 )=m(x-x_1 ) to get the value of m. 2nd, Find the intercept (b) by replacing p and x in the equation y=mx+b with one ordered pair and m with the slope. Then solve for b. 3rd , Write the equation by replacing m and b in the equation y=mx+b with the values you found. You answer will have an x and a p variable. (This is a skill learned in MAT116)(2 pts)
Slope: m=
Intercept: b=
Equation: P=

1)

(36,30)
(41,15)

2)m = (15-30))/(41-36) = -15/5 = -3
(p - 30) = -3(x - 36)
p - 30 = -3 x + 108
p = -3 x + 138
===================================
check
? (hopefully 15) = -3(41) + 138 ?
? = 15 yes

To find the two ordered pairs, we can use the given information. At a price of $30, the company sells 36 tiles per month. This can be written as (36, 30). At a price of $15, the company sells 41 tiles per month. This can be written as (41, 15).

To find the slope (m), we can use the slope formula:

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

Using the points (36, 30) and (41, 15), we substitute the values into the formula:

m = (15 - 30) / (41 - 36)
= (-15) / 5
= -3

The slope (m) is -3.

To find the intercept (b), we can use one of the ordered pairs and the slope in the equation y = mx + b. Let's use the point (36, 30):

30 = -3 * 36 + b

Simplifying:

30 = -108 + b
b = 30 + 108
b = 138

The intercept (b) is 138.

Now, we can substitute the slope (m) and intercept (b) into the equation y = mx + b:

P = -3x + 138

The equation for the demand equation is P = -3x + 138.