On itv's homework hotline, it's time for "rudolf's rules." if you guess what rule rudolf is using you get a prize. someone puts golf balls into a miniature-golf display called rudolf, then rudolf sends back a certain number of golf balls. today rudolf gets 8 balls and sends back 6. next rudolf gets 15 and sends back 27. when he gets 25, 57 are returned. if n represents the number of balls initially given to rudolf, write an expression to represent how many balls he sent back.

y = 3x -18 ( where y =  balls sent back by Rudolf; x= balls  given to Rudolf)

Step-by-step explanation:

x (Balls given)       y( Balls sent back)

8                             6                    Δy/Δx  = (27-6)/(15-8) =  3

15                            27

25                           57                 Δy/Δx  = (57-27)/(25-15) =  3

Observing the number sequence shows constant gradient and as such we can use equation of a straight line to relate the two variables.

Using the equation of a straight line we have:

(y-y1)/(x-x1) =  (y2-y1)/(x2-x1)

y-6/x-8  =       (27-6)/(15-8)

y-6/x-8  =    3

y-6        =  3(x-8)

y-6  = 3x - 24

y = 3x-18