Answer:
The function represents a direct variation
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
or 
In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m
Let
------> the line passes through the origin

Find the value of k------> substitute the value of x and y
-----> 

Find the value of k------> substitute the value of x and y
-----> 

Find the value of k------> substitute the value of x and y
-----> 

Find the value of k------> substitute the value of x and y
-----> 
The value of k is equal in all the points of the table and the line passes through the origin
therefore
The function represents a direct variation
the equation of the direct variation is equal to

All you do is divide -12/20 by 4/4 which is -3/5
K(cannot equal (the = sign with the line through it) -2
k(=/)-2
Answer:
236
Step-by-step explanation:
We assume the cost is a linear function of the number of lessons. That means the slope is the same everywhere.
Let (lessons, cost) = (x, y). We have (4, 84), (8, 160), (12, y3).
(y2 -y1)/(x2 -x1) = (y3 -y2)/(x3 -x2)
(160 -84)/(8 -4) = (y3 -160)/(12 -8)
76 = y3 -160
y3 = 160 +76 = 236
The cost will be $236 for 12 lessons.
__
The cost function is ...
y = 19x +8 . . . . for x lessons