Question

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if it builds 20 houses in this particular development, it can sell them for $540,000 each, but if it builds 50 houses, it will only be able to get $450,000 each. Obtain a linear demand equation. HINT [See Example 3.] (Let p be the price of a house and q the number of houses

Answer 1

We are assuming that p is the price of the house and that q is the number of the houses.

The points given (q,p) , therefore, are:
(20 , 540000) and (50 , 450000)

The general form of the linear straight line is:
y = mx+c where m is the slope and c is the y-intercept.

(1) Calculating the slope:
The formula used to calculate the slope is:
m = (y2-y1) / (x2-x1) where:
y2 is the y-coordinate of the second point = 450000
y1 is the y-coordinate of the first point = 540000
x2 is the x-coordinate of the second point = 50
x1 is the x-coordinate of the first point = 20
Therefore:
m = (450000-540000) / (50-40) = -3000

(2) Calculating the y-intercept:
After getting the slope, the equation now is:
y = -3000x + c
To get the value of thec, use any point that belongs to the line and substitute with it in the equation above. I will use the point (20, 540000).
y = -3000 + c
540000 = -3000(20) + c
c = 540000 + 3000(20) = 600000

Based on the above calculations, the equation of the line is:
y = -3000x + 600000