Question

solve the equation for y-value and choose whether it is a direct variation or inverse variation.
xy=7

a) y=7/x direct variation
b) y=x/7 direct variation
c) y=x/7 inverse variation
d) y=7/x inverse variation​

Answer 1

Given:

The equation is $xy=7$.

To find:

Whether the given equation is a direct variation or inverse variable.

Solution:

Direct variation: y is directly proportional to x.

$y\propto x$

$y=kx$

Inverse variation: y is inversely proportional to x.

$y\propto \dfrac{1}{x}$

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

Where, k is the constant of proportionality.

We have,

$xy=7$

Divide both sides by x.

$y=\dfrac{7}{x}$

It is in the form of inverse variation.

Since $y=\dfrac{7}{x}$ and it is inverse variation, therefore the correct option is (d).