An inverse variation includes the points (8, 2) and (4, 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 between two variables. Identify the general form of inverse variation. In inverse variation, one variable is directly proportional to the reciprocal of the other. Inverse variation: y = k / xFind constant of variation: We know that the point (8, 2) lies on the inverse variation curve. Use this point to find the constant of variation k. Substitute 8 for x and 2 for y in y = k / x. 2 = k / 8Solve for k: Solve the equation to find the value of k. To isolate k, multiply both sides by 8. 2 × 8 = (k / 8) × 8 16 = kWrite inverse variation equation: We have found the constant of variation: k = 16 Write the inverse variation equation using the value of k. y = 16 / xFind n: We need to find n when x = 4. Substitute 4 for x in y = 16 / x to find n. n = 16 / 4 n = 4

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An inverse variation includes the points $(8,\,2)$ and $(4,\,n)$ . 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,\,2)

and

(4,\,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 point $(8, 2)$ lies on the inverse variation curve. $\newline$ Use this point to find the constant of variation $k$ . $\newline$ Substitute $8$ for $x$ and $2$ for $y$ in $y = k / x$ . $\newline$ $2 = k / 8$
Solve for k: Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $8$ . $2 \times 8 = \left(\frac{k}{8}\right) \times 8$ $16 = k$
Write inverse variation equation: We have found the constant of variation: $\newline$ $k = 16$ $\newline$ Write the inverse variation equation using the value of $k$ . $\newline$ $y = \frac{16}{x}$
Find $n$ : We need to find $n$ when $x = 4$ . $\newline$ Substitute $4$ for $x$ in $y = \frac{16}{x}$ to find $n$ . $\newline$ $n = \frac{16}{4}$ $\newline$ $n = 4$