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).

To find the equation of the line for the demand equation, we need to find the slope and y-intercept of the line. We can use the given points (42, $20) and (52, $10) to do this.

Let's start by finding the slope (m) using the formula:

m = (change in y) / (change in x)

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

Now, let's use one of the given points to find the y-intercept (b). We can choose (42, $20) for convenience.

Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the values of slope (m) and one point (x, y) to solve for b.

20 = (-1)(42) + b
20 = -42 + b
b = 20 + 42
b = 62

So, the equation of the line for the demand equation is:

p = -x + 62