An inverse variation includes the points (8, 1) and (2, n) . Find n. Write and solve an inverse variation equation to find the answer. n = _____

Understand Inverse Variation: Understand the concept of inverse variation. In an inverse variation, the product of the two variables is constant. This means that if one variable increases, the other decreases proportionally so that the product remains the same. The general form of an inverse variation is y = k / x, where k is the constant of variation.Find Constant of Variation: Use the given point (8, 1) to find the constant of variation k. Substitute x = 8 and y = 1 into the inverse variation equation y = k / x. 1 = k / 8 Now, solve for k by multiplying both sides by 8. 1 * 8 = k k = 8Write Inverse Variation Equation: Use the constant of variation k to write the inverse variation equation. Now that we know k = 8, the inverse variation equation is y = 8 / x.Find n for x=2: Use the inverse variation equation to find n when x = 2. Substitute x = 2 into the equation y = 8 / x. n = 8 / 2 n = 4

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An inverse variation includes the points $(8,\,1)$ 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,\,1)

and

(2,\,n)

. Find

n

\newline

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

\newline

n = \,\_\_\_\_

Understand Inverse Variation: Understand the concept of inverse variation. $\newline$ In an inverse variation, the product of the two variables is constant. This means that if one variable increases, the other decreases proportionally so that the product remains the same. $\newline$ The general form of an inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given point $(8, 1)$ to find the constant of variation $k$ . Substitute $x = 8$ and $y = 1$ into the inverse variation equation $y = \frac{k}{x}$ . $1 = \frac{k}{8}$ Now, solve for $k$ by multiplying both sides by $8$ . $1 \times 8 = k$ $k = 8$
Write Inverse Variation Equation: Use the constant of variation $k$ to write the inverse variation equation. $\newline$ Now that we know $k = 8$ , the inverse variation equation is $y = \frac{8}{x}$ .
Find $n$ for $x=2$ : Use the inverse variation equation to find $n$ when $x = 2$ . Substitute $x = 2$ into the equation $y = \frac{8}{x}$ . $n = \frac{8}{2}$ $n = 4$