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An inverse variation includes the points $(-12,\,4)$ 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

Full solution

Q. An inverse variation includes the points

(-12,\,4)

and

(-3,\,n)

. Find

n

.

\newline

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

\newline

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

Define Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We need to find the constant $k$ using the point $(-12, 4)$ .
Find Constant $k$ : Substitute $x = -12$ and $y = 4$ into the equation to find $k$ : $4 = \frac{k}{(-12)}$ .
Calculate $k$ : Multiply both sides by $–12$ to solve for $k$ : $4 \times (–12) = k$ .
Use $k$ to Find $n$ : Calculating $k$ gives us: $k = -48$ .
Substitute $k$ into Equation: Now we use the value of $k$ to find $n$ when $x = -3$ . The equation is $n = \frac{k}{(-3)}$ .
Calculate $n$ : Substitute $k = -48$ into the equation: $n = (-48) / (-3)$ .
Calculate $n$ : Substitute $k = -48$ into the equation: $n = (-48) / (-3)$ .Calculate $n$ : $n = 16$ .

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