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An inverse variation includes the points $(2,\ 4)$ 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,\ 4)

and

(1,\ n)

. Find

n

.

\newline

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

\newline

n

= _______

Identify general form of inverse variation: Given that there is an inverse variation that includes the points $(2, 4)$ and $(1, n)$ . Identify the general form of inverse variation. In inverse variation, the product of the two variables is constant. Inverse variation: $y = \frac{k}{x}$ where $k$ is the constant of variation.
Find constant of variation: We know that the point $(2, 4)$ lies on the inverse variation curve. $\newline$ Use the point to find the constant of variation $k$ . $\newline$ Substitute $2$ for $x$ and $4$ for $y$ in $y = k / x$ . $\newline$ $4 = k / 2$
Solve for $k$ : Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $2$ . $4 \times 2 = (k / 2) \times 2$ $8 = k$ Now we have found the constant of variation $k$ .
Find $n$ value: Use the constant of variation $k$ to find $n$ when $x = 1$ . The inverse variation equation is $y = \frac{k}{x}$ . Substitute $k = 8$ and $x = 1$ into the equation. $y = \frac{8}{1}$ $y = 8$ So, $n = 8$ .

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