# How do you determine the constant of proportionality if y is inversely proportional to x and y = 6 when x = 4?

Apr 9, 2018

$k = 24$

#### Explanation:

y∝1/x,

$y = \frac{k}{x}$, where $k$ is constant

$y = 6$ $x = 4$ so,

$6 = \frac{k}{4}$

$6 \cdot 4 = k$

$k = 24$

Apr 9, 2018

$k = 24$

#### Explanation:

$\text{the initial statement is } y \propto \frac{1}{x}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow y = k \times \frac{1}{x} = \frac{k}{x}$

$\text{to find k use the given condition}$

$y = 6 \text{ when } x = 4$

$y = \frac{k}{x} \Rightarrow k = y x = 6 \times 4 = 24$