Please help me understand the formula and answer

Question

A clothing business finds there is a linear relationship between the number of shirts, nn, it can sell and the price, pp, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $5. Find a linear equation in the form p(n)= mn+b that gives the price pp they can charge for n shirts.

 

Because this answer involves an expression that is more complex than a whole number times nn, remember to type in multiplication symbols *. For example, if you wanted to enter 12n12n, type this in as (1/2)*n.

 

Answer 1

If you graphed and connected the two points with no. shirts on the y-axis and price/shirt on the x-axis you'd get a straight line with negative slope (the higher the price, the fewer you sell and v.v.)

Slope is rise/run (3000 - 1000)/(5 - 30) = 2000/-25 = -80 (that's m)

p(n) = mn + b 3000 = -80(5) + b, so b = 3,400 p(n) = -80n + 3400

or 1000 = -80(30) + b, so b also = 3,400 (if you gave away the shirts for free, you'd give 3,400. Doesn't quite make sense because in the real world things aren't to linear!)