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An inverse variation includes the points $(8,\,1)$ and $(2,\,n)$ . Find $n$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $n = \,\_\_\_\_$

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Write and solve inverse variation equations

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Q. An inverse variation includes the points

(8,\,1)

and

(2,\,n)

. Find

n

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

n = \,\_\_\_\_

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 if one variable increases, the other decreases proportionally so that the product remains the same. $\newline$ 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 point $(8, 1)$ to find the constant of variation $k$ . Substitute $x = 8$ and $y = 1$ into the inverse variation equation $y = \frac{k}{x}$ . $1 = \frac{k}{8}$ Now, solve for $k$ by multiplying both sides by $8$ . $1 \times 8 = k$ $k = 8$
Write Inverse Variation Equation: Use the constant of variation $k$ to write the inverse variation equation. $\newline$ Now that we know $k = 8$ , the inverse variation equation is $y = \frac{8}{x}$ .
Find $n$ for $x=2$ : Use the inverse variation equation to find $n$ when $x = 2$ . Substitute $x = 2$ into the equation $y = \frac{8}{x}$ . $n = \frac{8}{2}$ $n = 4$

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