Question

This relation is an inverse variation. {(–1, 8), (4, –2), (–2, 4)} Which equation represents this relation?

Answer 1

Answer:

$y = -\frac{8}{x}$

Step-by-step explanation:

Given

Inverse Variation:

$Points: \{(-1, 8), (4, -2), (-2, 4)\}$

Required

Determine the equation of the relation

An inverse relation is represented as:

$y = \frac{k}{x}$

Where k = constant of variation

Make k the subject:

$k = xy$

When x = -1, y = 8

So, we have:

$k = -1 * 8$

$k = -8$

When x = 4, y = -2

$k = 4 * -2$

$k = -8$

When x = -2, y = 4

$k= -2 * 4$

$k = -8$

From above calculations, we've established that:

$k = -8$

Substitute -8 for k in $y = \frac{k}{x}$

$y = \frac{-8}{x}$

$y = -\frac{8}{x}$

Hence, the equation is:

$y = -\frac{8}{x}$