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In an inverse variation, $y = 3$ when $x = 4$ . 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 = 3

when

x = 4

. 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 Equation: Identify the equation that represents inverse 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. The general form of an inverse variation is: $\newline$ $y = \frac{k}{x}$ $\newline$ where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation $k$ . $\newline$ We are given that $y = 3$ when $x = 4$ . We can substitute these values into the inverse variation equation to find $k$ : $\newline$ $3 = \frac{k}{4}$ $\newline$ To solve for $k$ , multiply both sides of the equation by $4$ : $\newline$ $3 \times 4 = k$ $\newline$ $k = 12$
Write Equation with Constant: Write the inverse variation equation using the value of $k$ . $\newline$ Now that we have found $k = 12$ , we can write the inverse variation equation as: $\newline$ $y = \frac{12}{x}$ $\newline$ This equation shows the relationship between $x$ and $y$ in an inverse variation where $y = 3$ when $x = 4$ .

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