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In an inverse variation, $y = 3$ when $x = 12$ . 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 = 3

when

x = 12

. Write an inverse variation equation that shows the relationship between

x

and

y

.

\newline

Write the equation using a decimal or an integer.

\newline

\_\_

Understand Inverse Variation: Understand the concept of inverse variation. $\newline$ In an inverse variation, the product of the two variables is constant. This means that as one variable increases, the other decreases proportionally. The general form of an inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation. $\newline$ We are given that $y = 3$ when $x = 12$ . We can substitute these values into the inverse variation equation to find $k$ . $\newline$ Equation: $y = \frac{k}{x}$ $\newline$ Substitute $3$ for $y$ and $12$ for $x$ : $3 = \frac{k}{12}$
Solve for $k$ : Solve for the constant of variation, $k$ . To find $k$ , multiply both sides of the equation by $12$ : $3 = \frac{k}{12}$ $3 \times 12 = k$ $k = 36$
Write Inverse Variation Equation: Write the inverse variation equation using the found constant of variation. $\newline$ Now that we have found $k$ to be $36$ , we can write the inverse variation equation as: $\newline$ $y = \frac{k}{x}$ $\newline$ $y = \frac{36}{x}$

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