Answer:
Indirect variation
Rule: [tex]y = \frac{18}{x}[/tex]
Step-by-step explanation:
Given
[tex]x \to 2,3,4,5[/tex]
[tex]y \to 9,6,4.5,3.6[/tex]
Required
Determine the type of variation
For direct variation, we have:
y increases, as x increases
In the above function, y decreases, as x increases
Hence, it is not a direct variation
Indirect variation.
In an indirect variation, y decreases, as x increases
And the equation is given as:
[tex]y = \frac{k}{x}[/tex]
Make k the subject
[tex]k =xy[/tex]
Where k is the constant of variation.
For:
[tex](x,y) = (2,9)[/tex]
[tex]k = 2 * 9 = 18[/tex]
For:
[tex](x,y) = (3,6)[/tex]
[tex]k = 3 * 6 = 18[/tex]
For every other values;
[tex]k = x * y = 18[/tex]
Hence, it is an indirect variation.
The rule is:
[tex]y = \frac{k}{x}[/tex]
Substitute 18 for k
[tex]y = \frac{18}{x}[/tex]
