Question

A company makes greeting cards and their research shows that that price and demand are related linearly: p=mx +b.They know that for every additional card they wish to sell they need to drop the price by $0.05. They also know that in order to sell 300 cards they need to set the price at $7. Find the linear equation relating P price to demand. Preview p =

Answer 1

P= -0.05q+22

Explanation:

To find the linear equation that relates price with quantity demanded, first we must find the slope. Because the independent variable is the quantity demanded and the dependent variable is the price, the slope represents how the price changes when there is an extra unit of quantity demanded. The problem gives this information: "for every additional card (extra unit) they need to drop the price by $0.05". The slope (m) in this case is negative because an extra unit, reduces the price: -0.05

The second step is to use this formula:

Y-y1= m*(X-x1)

y1 and x1 is a point of the demand curve, in this case it is y1= $7 and x1=300

Y-$7= -$0.05*(X-300)

Y-7=-0.05X+15

Y= -0.05X+15+7

Y= -0.05X-22

Price= -0.05 quantity demanded +22