A clothing business finds there is a linear relationship between the number of shirts it can sell and the price. Create a linear equation of this representation

Question

A clothing business finds there is a linear relationship between the number of shirts,,it can sell and the price,, it can charge per shirt. In particular, historical data shows that  shirts can be sold at a price of , while  shirts can be sold at a price of . Give a linear equation in the form  that gives the price  they can charge for  shirts.

Answer 1

You want p(n) = mn+b where p(n) and n are given their meaning in the problem, m is the slope of this linear relationship and b is the p(n) intercept of the relationship (where n=0).

Solutions to this linear equation maybe represented by an ordered pair (n, p(n))

Your given two such solutions

(7000,93) and (17000,13).

Find the slope by dividing the change in price p(n) by the change in shirts n, i.e.

m= (93-13) / (17000-7000)

Use the found m above and either point given to substitute into

p(n)=mx+b

this will leave you with b to solve for. Once you found b, you’ve got the two needed parameters of the equation p(n)=mn +b. So replace m and b with what you find in the calculations and you’re done.