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In an inverse variation, $y = 1$ when $x = 16$ . 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 = 16

. 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 type of variation: Identify the type of variation. $\newline$ In an inverse variation, the product of the two variables is constant. This means that as one variable increases, the other decreases proportionally. $\newline$ 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 values to find the constant of variation. $\newline$ We are given that $y = 1$ when $x = 16$ . We can substitute these values into the inverse variation equation to find $k$ . $\newline$ $1 = \frac{k}{16}$
Solve for constant of variation: Solve for the constant of variation, $k$ . To find $k$ , we multiply both sides of the equation by $16$ . $1 \times 16 = \frac{k}{16} \times 16$ $16 = k$
Write inverse variation equation: Write the inverse variation equation using the value of $k$ . Now that we know $k$ is $16$ , we can write the inverse variation equation as: $y = \frac{16}{x}$

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