An inverse variation includes the points (3, 2) and (1, 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. Inverse variation: y = k / xSubstitute Point (3, 2): We know that the point (3, 2) lies on the inverse variation curve. Substitute x = 3 and y = 2 into the inverse variation equation to find the constant of variation k. 2 = k / 3Solve for Constant: Solve the equation to find the value of k. Multiply both sides by 3 to isolate k. 2 * 3 = k k = 6Write Inverse Variation Equation: Now that we have the constant of variation, we can write the inverse variation equation. Substitute k = 6 into y = k / x. y = 6 / xFind n for x = 1: We need to find n when x = 1. Substitute x = 1 into the inverse variation equation y = 6 / x. n = 6 / 1 n = 6

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An inverse variation includes the points $(3,\,2)$ and $(1,\,n)$ . 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

(3,\,2)

and

(1,\,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. $\newline$ Inverse variation: $y = \frac{k}{x}$
Substitute Point $(3, 2)$ : We know that the point $(3, 2)$ lies on the inverse variation curve. $\newline$ Substitute $x = 3$ and $y = 2$ into the inverse variation equation to find the constant of variation $k$ . $\newline$ $2 = \frac{k}{3}$
Solve for Constant: Solve the equation to find the value of $k$ . Multiply both sides by $3$ to isolate $k$ . $2 \times 3 = k$ $k = 6$
Write Inverse Variation Equation: Now that we have the constant of variation, we can write the inverse variation equation. $\newline$ Substitute $k = 6$ into $y = \frac{k}{x}$ . $\newline$ $y = \frac{6}{x}$
Find $n$ for $x = 1$ : We need to find $n$ when $x = 1$ . Substitute $x = 1$ into the inverse variation equation $y = \frac{6}{x}$ . $n = \frac{6}{1}$ $n = 6$