Help with word problem

Question

At a unit price of $55 , the quantity demanded of a certain commodity is 1000 units. At a unit price of $85, the demand drops to 600 units. A) given that it is linear , find the demand equation. B) graph the demand equation. C)above which price will there be no demand? D) what is the maximum quantity demanded? E) what is the quantity demanded when the unit price is $65? F) what is the slope of the demand equation? What dose the slope mean in terms of the quantity demanded and dollars?

Answer 1

Hello Laurie, 

 

The general form of a linear equation is (y - y0) = m * (x - x0). This produces the slope equation m = (y1 - y0)/(x1-x0).

 

For your problem, x0 = $55, y0 = 1000, x1 = $85, y1 = 600. 

 

m = (600 - 1000)/(85 - 55) = -13.33 units/$

 

Now, plugging this slope in the general form, we have: 

 

(y - y0) = -13.33*(x-x0)

 

Choose either point, (x0,y0) or (x1,y1), and plug into this general form. 

 

(y - 1000) = -13.33*(x-55) 

y = -13.33*x +1733.15

 

I believe this will give you a strong start on this problem.