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An inverse variation includes the points $(6,\,1)$ and $(3,\,n)$ . 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

(6,\,1)

and

(3,\,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 if $y$ varies inversely with $x$ , then $xy = k$ for some constant $k$ .
Find Constant $k$ : Use the given point $(6, 1)$ to find the constant $k$ . Substitute $x = 6$ and $y = 1$ into the inverse variation equation $xy = k$ . $6 \times 1 = k$ $k = 6$
Use Constant $k$ : Use the constant $k$ to find $n$ when $x = 3$ . We know that $k = 6$ and the inverse variation equation is $xy = k$ . Substitute $k = 6$ and $x = 3$ into the equation to find $n$ . $3 \times n = 6$
Solve for n: Solve for n. $\newline$ Divide both sides of the equation by $3$ to isolate n. $\newline$ $n = \frac{6}{3}$ $\newline$ $n = 2$

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