# Suppose y varies inversely with x. How do you write an equation for the inverse variation for Y = 4 when x = 2.5?

May 16, 2016

$y = \frac{10}{x} \text{ "larr" } 4 = \frac{10}{2.5}$

#### Explanation:

Varies inversely$\text{ "->" } y = \frac{k}{x}$

Where $k$ is the constant of variation (conversion factor)

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$\textcolor{p u r p \le}{\text{Determine the value of } k}$

Using the given condition:

color(brown)(" "y=k/xcolor(blue)(" "->" "4=k/2.5))

Multiply both sides by $2.5$

$\text{ } 4 \times 2.5 = k \times \frac{2.5}{2.5}$

But $\frac{2}{5} / 2.5 = 1$

$\text{ } k = 10$
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$\textcolor{b r o w n}{\text{ "y=k/xcolor(blue)(" "->" } y = \frac{10}{x}}$