Answer:
- Inverse Variation
- Equation: [tex]XY = 12[/tex]
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;
[tex]Y = kX[/tex]where k is the constant of variation
Make k the subject of formula
[tex]k = \frac{Y}{X}[/tex]
When Y = 6, X= 2
[tex]K = \frac{6}{2} = 3[/tex]
When Y = 3, X = 4
[tex]K = \frac{3}{4}[/tex]
There's no need to check further as both values of k are not equal
To check for inverse variation;
[tex]Y = \frac{k}{X}[/tex]
Make k the subject of formula
[tex]k = YX[/tex]
When Y = 6, X= 2
[tex]K = 6 * 2 = 12[/tex]
When Y = 3, X = 4
[tex]K = 3 * 4 = 12[/tex]
When Y = 3/2; X = 8
[tex]K = \frac{3}{2} * 8 = \frac{24}{2} = 12[/tex]
When Y = 1, X = 12
[tex]K = !2 * 1 = 12[/tex]
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 [tex]k = YX[/tex]
Substitute 12 for k
So, the equation becomes
[tex]12 = XY[/tex]
Reorder
[tex]XY = 12[/tex]
Hence, the equation is [tex]XY = 12[/tex]
