SOLUTION: A company makes t-shirts and their research shows that that price and demand are related linearly: p = m x + b . p=mx+b. They know that in order to sell 5 shirts they nee

Decreasing the price in 42-32 = 10 dollars increases the demand in 5 shirts, from 5 to 10.


Hence, the slope of the straight line of the demand function is   = 0.5.


Then the function itself is


    d(p) = 5 - 0.5(p - 42).   (1)


CHECK it :  at p= 42 you have  d(p) = 5.   ! Correct !

            at p= 32 you have  d(p) = 5 - 0.5*(32-42) = 5 - 0.5*(-10) = 5 + 5 = 10.   ! Correct !


You can transform the function (1) to the form


    d(p) = 5 - 0.5p + 21,   or   d(p) = 26 - 0.5p.   Thus,  m = -0.5,  b = 26.   ANSWER