Question

6) A demand curve for a product is the number of items the consumer will buy at different prices. At a price of $2 a store can sell 2400 of a particular type of toy truck. At a price of $8 the store can sell 600 such trucks. If x represents the price of trucks and y the number of items sold, write an equation for the demand curve.

Answer 1

Given :

When price is $2 dollars he sells 2400 units .

When price is $8 dollars he sells 600 units .

To Find :

If x represents the price of trucks and y the number of items sold, write an equation for the demand curve.

Solution :

Two points are given :

$(x_1,y_1)=(2,2400)$

$(x_2,y_2)=(8,600)$

Now , slope is given by :

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{2400-600}{2-8}\\\\m=\dfrac{-1800}{6}\\\\m=-300$

Now , the equation of line containing these two points and slope -300 is :

$(y-y_1)=m(x-x_1)\\\\y-600=-300(x-8)\\\\y=-300x+2400+600\\\\y=-300x+3000$

Therefore , equation for the demand curve is $y = -300x +3000$ .

Hence , this is the required solution .