Linear equations

Question

A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 2000 shirts can be sold at a price of $79, while 6000 shirts can be sold at a price of $43. Give a linear equation in the form p=mn+b that gives the price p they can charge for n shirts.

Answer 1

Hi Nell,

The problem essentially gives you two points (x1,y1) = (2000,79) and (x2,y2) = (6000,43) which lie on the line. You can use these two points to calculate the slope:

m = rise/run = (y2-y1)/(x2-x1)

and then use the point slope equation for a line:

y= m(x - x1) + y1

You will have to multiply this out to get the exact form requested from the problem.

I hope that helps!