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 15 20
y 20 15 2 2

a. inverse variation;y=10/x
b. neither
c. direct variation; y=x+10
d. direct variation; y=10x

If xy is constant, it's inverse

If x/y is constant, it's direct

Looks like (b) to me

(c) is a bogus answer in any case.

Thanks for the great explanation steve

it is B. neither

i think its neither

d. direct variation; y=10x

To determine the relationship between the variables in the table, we can analyze the values of x and y.

In a direct variation, as x increases, y also increases or decreases by a constant ratio. In an inverse variation, as x increases, y decreases or increases by a constant ratio.

Let's observe the table:

x 2 5 15 20
y 20 15 2 2

As x increases from 2 to 5, y decreases from 20 to 15, indicating an inverse relationship. However, when x increases from 5 to 15, y decreases further from 15 to 2, but not by a constant ratio. This breaks the pattern of an inverse variation.

Therefore, we can conclude that the relationship between the variables in the table is neither a direct nor inverse variation.

There is no single function that can accurately model the relationship between x and y in the given table.

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

a. inverse variation;y=60/x
b. neither
c. direct variation; y=2x+2
d. direct variation; y=15x