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An inverse variation includes the points $(4,\,1)$ 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

Full solution

Q. An inverse variation includes the points

(4,\,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 if $y$ varies inversely with $x$ , then $xy = k$ for some constant $k$ .
Find Constant $k$ : Use the given point $(4, 1)$ to find the constant $k$ . Substitute $x = 4$ and $y = 1$ into the inverse variation equation $xy = k$ . $4 \times 1 = k$ $k = 4$
Use Point $(4, 1)$ : Use the constant $k$ to find $n$ when $x = 2$ . $\newline$ We know that $k = 4$ and the inverse variation equation is $xy = k$ . Substitute $k = 4$ and $x = 2$ into the equation to find $n$ . $\newline$ $2 \cdot n = 4$
Find $n$ for $x=2$ : Solve for $n$ . $\newline$ Divide both sides of the equation by $2$ to isolate $n$ . $\newline$ $n = \frac{4}{2}$ $\newline$ $n = 2$

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