An inverse variation function is of the form
[tex]y= \frac{k}{x} [/tex]
where is constant.
Because the function passes through (4, 5). therefore
[tex]5= \frac{k}{4} \\ or \\ k=20[/tex]
The required function is therefore
[tex]y= \frac{20}{x} \\ or \\ xy = 20 [/tex]
Verify that the function is correct because it should pass through the point (10, 2).
When x = 10, obtain
[tex]y= \frac{20}{10}=2 [/tex]
This verifies that the function is correct.
Answer: [tex]y= \frac{20}{x} \,\, or \,\, xy=20 [/tex]
