Answer:
[tex]y = -\frac{8}{x}[/tex]
Step-by-step explanation:
Given
Inverse Variation:
[tex]Points: \{(-1, 8), (4, -2), (-2, 4)\}[/tex]
Required
Determine the equation of the relation
An inverse relation is represented as:
[tex]y = \frac{k}{x}[/tex]
Where k = constant of variation
Make k the subject:
[tex]k = xy[/tex]
When x = -1, y = 8
So, we have:
[tex]k = -1 * 8[/tex]
[tex]k = -8[/tex]
When x = 4, y = -2
[tex]k = 4 * -2[/tex]
[tex]k = -8[/tex]
When x = -2, y = 4
[tex]k= -2 * 4[/tex]
[tex]k = -8[/tex]
From above calculations, we've established that:
[tex]k = -8[/tex]
Substitute -8 for k in [tex]y = \frac{k}{x}[/tex]
[tex]y = \frac{-8}{x}[/tex]
[tex]y = -\frac{8}{x}[/tex]
Hence, the equation is:
[tex]y = -\frac{8}{x}[/tex]
