Question

10. Is the relationship between the variables in the table a direct variation, an inverse variation,

both, or neither? If it is a direct or inverse variation, write a function to model it.
x 2 5 12 20
y 30 12 5 3

direct variation; y = 15x
60
inverse variation; y=
direct variation; y = 2x + 2
neither
X

Answer 1

Explanation:

For direct variation, an increase or decrease in one variable would lead to a corresponding increase or decrease in the other variable.

For inverse variation, an increase or decrease in one variable would lead to a corresponding decrease or increase in the other variable.

From the given table, as the value of x is increasing, the value of y is decreasing. It means that it is an inverse variation.

Assuming a constant of variation, k then,

y = k/x

k = yx

When y = 30 and x = 2,

k = 30 × 2 = 60

Therefore, the function to model the inverse variation is

y = 60/x