Two part question: Suppose a market research company finds that at a price of p=$25, they would sell x=56 tiles each month. If they lower the price to p=$20, then more people would purchase the tile, and they can expect to sell x=66 tiles in a month's time. Finf the equation of the line for the emand equation. Hint: write answer in the form p-mx+b
To find the equation of the demand equation, you can use the point-slope form of a linear equation. This form is given by:
y - y₁ = m(x - x₁)
In this case, the price (p) is the independent variable, and the quantity (x) is the dependent variable. We are given two points: (p₁, x₁) = (25, 56) and (p₂, x₂) = (20, 66).
To find the slope (m), you can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we get:
m = (66 - 56) / (20 - 25)
m = 10 / -5
m = -2
Now, let's substitute one of the points into the point-slope form equation. Let's choose (p₁, x₁) = (25, 56):
x - x₁ = m(p - p₁)
x - 56 = -2(p - 25)
Expanding and simplifying:
x - 56 = -2p + 50
Rearranging the equation to match the desired form p - mx + b:
-2p + x = -6
So the equation of the demand equation is p - mx + b = -6.