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, them 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 the answer in p = mx + b form.
To find the equation of the demand equation in the form p = mx + b, we need to determine the values of m and b.
We're given two sets of data: (p = $20, x = 42) and (p = $10, x = 52).
First, let's find the value of m, which represents the slope of the line.
The slope, m, can be calculated using the formula:
m = (change in y) / (change in x)
Given the two sets of data, the change in y is 52 - 42 = 10, and the change in x is $10 - $20 = -$10.
So, the slope, m, is:
m = (10) / (-10) = -1
Now let's find the value of b, which represents the y-intercept of the line.
We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the first data point (p = $20, x = 42), we have:
x1 = 42
y1 = $20
Substituting these values into the equation, we get:
p - $20 = -1(x - 42)
Simplifying further:
p - $20 = -x + 42
p = -x + 42 + $20
p = -x + $62
Finally, we can rewrite the equation in the desired form p = mx + b:
p = -x + $62
Therefore, the equation of the demand equation in p = mx + b form is p = -x + $62.