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An inverse variation includes the points $(2,\,3)$ and $(1,\,n)$ . 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

(2,\,3)

and

(1,\,n)

. Find

n

.

\newline

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

\newline

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

Identify General Form: Given that there is an inverse variation between two variables. $\newline$ Identify the general form of inverse variation. $\newline$ In inverse variation, one variable is directly proportional to the reciprocal of the other. $\newline$ Inverse variation: $y = \frac{k}{x}$
Find Constant of Variation: We know that the points $(2, 3)$ are part of the inverse variation. $\newline$ Use the given point to find the constant of variation $k$ . $\newline$ Substitute $2$ for $x$ and $3$ for $y$ in $y = \frac{k}{x}$ . $\newline$ $3 = \frac{k}{2}$
Solve for k: Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $2$ . $3 \times 2 = (k / 2) \times 2$ $6 = k$
Write Inverse Variation Equation: We have found that $k = 6$ . $\newline$ Write the inverse variation equation with the found value of $k$ . $\newline$ Substitute $k = 6$ into $y = \frac{k}{x}$ . $\newline$ $y = \frac{6}{x}$
Find $n$ : Use the inverse variation equation to find $n$ when $x = 1$ . Substitute $1$ for $x$ in $y = \frac{6}{x}$ . $n = \frac{6}{1}$ $n = 6$

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