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:6,3,3/2,1

Answer 1

- Inverse Variation

- Equation:
`XY = 12`

Explanation:

Given

X-> 2 | 4 | 8 | 12

Y-> 6 | 3 | 3/2 | 1

Required

- State the type of variation the table represents

- Determine the equation to model the data

To check for type of variation; we'll make use of trial by error method.

To start with; We'll check for direct variation.

This is done using the following expression;

`Y = kX`where k is the constant of variation

Make k the subject of formula

`k = (Y)/(X)`

When Y = 6, X= 2

`K = (6)/(2) = 3`

When Y = 3, X = 4

`K = (3)/(4)`

There's no need to check further as both values of k are not equal

To check for inverse variation;

`Y = (k)/(X)`

Make k the subject of formula

`k = YX`

When Y = 6, X= 2

`K = 6 * 2 = 12`

When Y = 3, X = 4

`K = 3 * 4 = 12`

When Y = 3/2; X = 8

`K = (3)/(2) * 8 = (24)/(2) = 12`

When Y = 1, X = 12

`K = !2 * 1 = 12`

Note that for all values of X and Y, K remains constant;

Hence, the table represents an inverse direction

To determine the equation;

We make use of
`k = YX`

Substitute 12 for k

So, the equation becomes

`12 = XY`

Reorder

`XY = 12`

Hence, the equation is
`XY = 12`