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An inverse variation includes the points $(4,\,3)$ 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,\,3)

and

(2,\,n)

. Find

n

.

\newline

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

\newline

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

Identify general form: Given that the relationship between the variables is an inverse variation. $\newline$ Identify the general form of inverse variation. $\newline$ Inverse variation: $y = \frac{k}{x}$
Substitute point $(4, 3)$ : We know that the point $(4, 3)$ lies on the inverse variation curve. $\newline$ Substitute $x = 4$ and $y = 3$ into the inverse variation equation $y = \frac{k}{x}$ to find the constant of variation $k$ . $\newline$ $3 = \frac{k}{4}$
Solve for constant: Solve for $k$ by multiplying both sides of the equation by $4$ . $3 \times 4 = k$ $12 = k$ Now we have found the constant of variation $k$ .
Write inverse variation equation: Write the inverse variation equation using the constant of variation $k$ we found. $\newline$ Substitute $k = 12$ into $y = \frac{k}{x}$ . $\newline$ The inverse variation equation is $y = \frac{12}{x}$ .
Find $n$ for $x = 2$ : Use the inverse variation equation to find $n$ when $x = 2$ . Substitute $x = 2$ into $y = \frac{12}{x}$ . $n = \frac{12}{2}$ $n = 6$

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