# Suppose that y varies inversely with x. Write a function that models the inverse function. x = 7 when y = 3?

Mar 27, 2017

$y = \frac{21}{x}$

#### Explanation:

Inverse variation formula is $y = \frac{k}{x}$, where k is the constant and $y = 3$ and $x = 7$.

Substitute $x$ and $y$ values into the formula,

$3 = \frac{k}{7}$

Solve for k,

$k = 3 \times 7$
$k = 21$

Hence,

$y = \frac{21}{x}$

Mar 27, 2017

$y = \frac{21}{x}$

#### Explanation:

$y = k \cdot \frac{1}{x}$ , where $k$ is a constant.

$x = 7 , y = 3$, then

$3 = k \cdot \frac{1}{7}$

multiply with $7$ to both sides.

$7 \cdot 3 = k \cdot \frac{1}{7} \cdot 7$

$21 = k$

therefore it equation is

$y = 21 \cdot \frac{1}{x} = \frac{21}{x}$