Question

is the relationship between the variables in this table a direct variation, an inverse variation or neither. if it is a direct or inverse variation, write a function to model it. x: 2, 4, 6, 8 y: 1/3, 1/6, 1/9, 1/12

Answer 1

For this case we have that the relationship is inverse.
 Therefore, we have a function of the form:
 $y = \frac{k}{x}$
 We must find the value of k.
 For this, we use any ordered pair, such as:
 $(x, y) = (2, 1/3)$
 Substituting values:
 $\frac{1}{3} = \frac{k}{2}$
 Clearing k we have:
 $k = \frac{2}{3}$
 Then, the function is:
 $y = \frac{2}{3x}$
 Answer:
 The relationship between the variables in this table is an inverse variation.
 A function to model is:
 $y = \frac{2}{3x}$