Question

Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table. x 2 4 8 12 y 4 2 1 2/3

Answer 1

The equation for the direct variation is y= kx (where k is contant of variation.)

This equation represent that if x will increase then y will also increase because it's k times x.

Where the equation for indirect variation is $y=\frac{1}{k} x$

By this equation if x will increase then y will decrease and vice versa.

The given data is :

x: 2 4 8 12

y: 4 2 1 2/3

Notice as x is increasing then y is decreasing. Like x has increased from 2 to 4 then y is decresing from 4 to 2 and so on.

So, the given data represent an indirect variation.