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In an inverse variation, $y = 1$ when $x = 8$ . Write an inverse variation equation that shows the relationship between $x$ and $y$ . $\newline$ Write the equation using a decimal or an integer. $\newline$ $\_\_$

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Write inverse variation equations

Full solution

Q. In an inverse variation,

y = 1

when

x = 8

. Write an inverse variation equation that shows the relationship between

x

and

y

.

\newline

Write the equation using a decimal or an integer.

\newline

\_\_

Identify Inverse Variation: Which equation represents the inverse variation? $\newline$ In inverse variation, the product of the two variables is constant. This means that as one variable increases, the other decreases proportionally. $\newline$ Inverse variation equation: $y = \frac{k}{x}$
Substitute Values: We know that $y = 1$ when $x = 8$ . Substitute $8$ for $x$ and $1$ for $y$ in the inverse variation equation $y = \frac{k}{x}$ to find the constant of variation, $k$ . Equation after substitution: $1 = \frac{k}{8}$
Solve for Constant: Solve the equation $1 = \frac{k}{8}$ to find the value of $k$ . $\newline$ Multiply both sides of the equation by $8$ to isolate $k$ . $\newline$ $8 \times 1 = k$ $\newline$ $k = 8$
Write Inverse Variation Equation: Now that we have found the value of $k$ , we can write the inverse variation equation. $\newline$ Substitute $8$ for $k$ in $y = \frac{k}{x}$ . $\newline$ Inverse variation equation: $y = \frac{8}{x}$

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