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In an inverse variation, $y = 4$ when $x = 8$ . 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 = 4

when

x = 8

. 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 Inverse Variation Equation: Identify the equation that represents 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: $\newline$ $y = \frac{k}{x}$ $\newline$ 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 $y = 4$ when $x = 8$ . We can substitute these values into the inverse variation equation to find $k$ . $\newline$ $4 = \frac{k}{8}$ $\newline$ Now, solve for $k$ by multiplying both sides by $8$ . $\newline$ $k = 4 \times 8$ $\newline$ $k = 32$
Write Inverse Variation Equation: Write the inverse variation equation using the constant of variation. $\newline$ Now that we have found $k = 32$ , we can write the inverse variation equation as: $\newline$ $y = \frac{32}{x}$ $\newline$ This equation shows the relationship between $x$ and $y$ for this inverse variation.

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