An inverse variation includes the points (8, 3) and (2, n) . Find n. Write and solve an inverse variation equation to find the answer. n = _____

Identify General Form: Given that there is an inverse variation relationship between two variables. Identify the general form of inverse variation. In inverse variation, the product of the two variables is constant. Inverse variation: y = k / x where k is the constant of variation.Find Constant of Variation: We know that the point (8, 3) lies on the inverse variation curve. Use this point to find the constant of variation k. Substitute 8 for x and 3 for y in y = k / x. 3 = k / 8Solve for Constant: Solve the equation to find the value of k. To isolate k, multiply both sides by 8. 3 × 8 = (k / 8) × 8 24 = k Now we have found the constant of variation k.Substitute and Calculate: We have the inverse variation equation: y = 24 / x Now we need to find n when x = 2. Substitute 2 for x in y = 24 / x. n = 24 / 2Final Value Calculation: Calculate the value of n. n = 24 / 2 n = 12 We have found the value of n.

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An inverse variation includes the points $(8, 3)$ and $(2, n)$ . Find $n$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $n = \_\_\_\_$

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Algebra 1

Write and solve inverse variation equations

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Q. An inverse variation includes the points

(8, 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 there is an inverse variation relationship between two variables. $\newline$ Identify the general form of inverse variation. $\newline$ In inverse variation, the product of the two variables is constant. $\newline$ Inverse variation: $y = \frac{k}{x}$ where $k$ is the constant of variation.
Find Constant of Variation: We know that the point $(8, 3)$ lies on the inverse variation curve. $\newline$ Use this point to find the constant of variation $k$ . $\newline$ Substitute $8$ for $x$ and $3$ for $y$ in $y = k / x$ . $\newline$ $3 = k / 8$
Solve for Constant: Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $8$ . $3 \times 8 = (k / 8) \times 8$ $24 = k$ Now we have found the constant of variation $k$ .
Substitute and Calculate: We have the inverse variation equation: $\newline$ $y = \frac{24}{x}$ $\newline$ Now we need to find $n$ when $x = 2$ . $\newline$ Substitute $2$ for $x$ in $y = \frac{24}{x}$ . $\newline$ $n = \frac{24}{2}$
Final Value Calculation: Calculate the value of $n$ . $n = \frac{24}{2}$ $n = 12$ We have found the value of $n$ .