An inverse variation includes the points (16, 3) 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 inverse of the other. Inverse variation: y = k / xFind constant of variation: We know that the point (16, 3) lies on the inverse variation curve. Use this point to find the constant of variation k. Substitute 16 for x and 3 for y in y = k / x. 3 = k / 16Solve for k: Solve the equation to find the value of k. To isolate k, multiply both sides by 16. 3 × 16 = (k / 16) × 16 48 = kWrite inverse variation equation: We have found k = 48. Write the inverse variation equation with the found value of k. Substitute k = 48 into y = k / x. y = 48 / xFind n: We need to find n when x = 4. Substitute 4 for x in y = 48 / x to find n. n = 48 / 4 n = 12

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An inverse variation includes the points $(16,\,3)$ 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

(16,\,3)

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 inverse of the other. $\newline$ Inverse variation: $y = \frac{k}{x}$
Find constant of variation: We know that the point $(16, 3)$ lies on the inverse variation curve. $\newline$ Use this point to find the constant of variation $k$ . $\newline$ Substitute $16$ for $x$ and $3$ for $y$ in $y = k / x$ . $\newline$ $3 = k / 16$
Solve for k: Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $16$ . $3 \times 16 = \left(\frac{k}{16}\right) \times 16$ $48 = k$
Write inverse variation equation: We have found $k = 48$ . $\newline$ Write the inverse variation equation with the found value of $k$ . $\newline$ Substitute $k = 48$ into $y = \frac{k}{x}$ . $\newline$ $y = \frac{48}{x}$
Find $n$ : We need to find $n$ when $x = 4$ . $\newline$ Substitute $4$ for $x$ in $y = \frac{48}{x}$ to find $n$ . $\newline$ $n = \frac{48}{4}$ $\newline$ $n = 12$