A Store cells packages of comic books with a poster.
a) Write a linear function in the form y= mx + b that represents the cost , y, of a package containing any number of comic books ,x.
b) Suppose another store sells a similar package , modelled by a linear function with initial value $ 7.99 . Which store has the better deal? Explain.

The correct answer is: a) y = x + 6.75, b) First case

 No of comic books = x
Cost of the package = y
In the figure, cost of 1 poster and 6 comics = $12.75
i.e. x  = 6 , y = 12.75
And cost of 1 poster and 13 comics = $19.75
i.e. x = 13 , y = 19.75
( Since 1 poster is given in every package we will not count it while forming linear function. But we will notice further that the cost of the poster will act as an intercept in the equation.)
(a) Now, using two – point form, equation of the line is
(y – y₁) = m (x – x₁)  where  m =

 m =  

         =    = 1
Now,  equation of the line is (y – y₁) = m (x – x₁)
(y – 12.75) = 1 (x – 6)
y – 12.75 = x – 6
y =  x – 6 + 12.75
y = x + 6.75

(b) It is given that initial cost = $7.99
Notice that shop sells 1 poster with x no of comic books. So, initial cost means cost of 1 poster and 1 comic book.
Cost of 1 poster + 1 comic book = $7.99
In the previous case, Total cost was given by : y  = x + 6.75
Put x = 1
Cost of 1 poster + 1 comic book = Total cost = 1 + 6.75

= $7.75  <  $7.99
Since the total cost in first case ( i.e. (a) part)  is lesser, it has the best deal.