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In an inverse variation, $y = 2$ when $x = 9$ . Write an inverse variation equation that shows the relationship between $x$ and $y$ . $\newline$ Write the equation using a decimal or an integer. $\newline$ $\_\_$

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Write inverse variation equations

Full solution

Q. In an inverse variation,

y = 2

when

x = 9

. Write an inverse variation equation that shows the relationship between

x

and

y

.

\newline

Write the equation using a decimal or an integer.

\newline

\_\_

Identify Form: Identify the form of the inverse variation equation. $\newline$ In an inverse variation, the product of the two variables is constant. The general form of an inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant: Use the given values to find the constant of variation $k$ . We are given that $y = 2$ when $x = 9$ . Substitute these values into the inverse variation equation to find $k$ . $2 = \frac{k}{9}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $9$ . $\newline$ $2 \times 9 = k$ $\newline$ $18 = k$
Write Equation: Write the inverse variation equation using the value of $k$ . $\newline$ Now that we have found $k$ to be $18$ , substitute it back into the general form of the inverse variation equation. $\newline$ $y = \frac{18}{x}$

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