SOLUTION: A company makes t-shirts and their research shows that that price and demand are related linearly:p=mx+b.They know that in order to sell 5 shirts they need to set the price at $37,

The demand function is the number of sold items as a function of price.


The slope of the demand function is the ratio of the increment of the number of the sold items to the increment of the price.


In this case, the increment of the number of the sold items is  5 - 15 = -10  and 

              the increment of the price is  37-17 = 20 dollars.


Therefore, the slope is   = -0.5 item per dollar.


Hence, the requested demand function is  d(p) = 5 - 0.5*(p-37).    (1)


CHECK.  At p = 37,  d(p) = d(37) = 5 - 0.5*(37-37) = 5 - 0.5*0 = 5 - 0 = 5 items.   ! Correct !

        At p = 17,  d(p) = d(17) = 5 - 0.5*(17-37) = 5 - 0.5*(-20) = 5 + 0.5*20 = 5 + 10 = 15 items.   ! Correct !