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

Answer:

- Inverse Variation

- Equation: $XY = 12$

Step-by-step 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

$k = \frac{Y}{X}$

When Y = 6, X= 2

$K = \frac{6}{2} = 3$

When Y = 3, X = 4

$K = \frac{3}{4}$

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

To check for inverse variation;

$Y = \frac{k}{X}$

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

$K = \frac{3}{2} * 8 = \frac{24}{2} = 12$

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 $XY = 12$