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 =

p = - 0.05m + 22

Step-by-step explanation:

As given in question,

The relation between the price and demand can be given by,

p=mx + b

where is p is price and x is demand.

Since in order to sell 300 cards the price has to be fix at $7.

So,

7 = 300m+b (1)

And for every additional card they need to drop the price by $0.05.

So,

7-0.05 = 301m+b

=>6.95 = 301m + b (2)

Subtracting equation (1) from equation (2), we will have

6.95 - 7 = 301m - 300m

=>m = - 0.05

By putting the value of m in equation (1), we get

7 = 300. (-0.05) + b

=> b = 22

So, the linear equation that show the relation between price and demand is given by

p = - 0.05m + 22