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In an inverse variation, $y = 4$ when $x = 6$ . Write an inverse variation equation that shows the relationship between $x$ and $y$ . Write the equation using a decimal or an integer. $\_\_\_\_$

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Write and solve inverse variation equations

Full solution

Q. In an inverse variation,

y = 4

when

x = 6

. Write an inverse variation equation that shows the relationship between

x

and

y

. Write the equation using a decimal or an integer.

\_\_\_\_

Identify general form: Identify the general form of an inverse variation equation, which is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Substitute given values: Substitute the given values of $y$ and $x$ into the inverse variation equation to find the constant of variation $k$ . We have $y = 4$ when $x = 6$ , so we substitute these values into the equation to get $4 = \frac{k}{6}$ .
Solve for k: Solve for k by multiplying both sides of the equation by $6$ to isolate $k$ . This gives us $4 \times 6 = k$ , which simplifies to $k = 24$ .
Substitute $k$ back: Substitute the value of $k$ back into the general form of the inverse variation equation to get the specific equation for this problem. With $k = 24$ , the equation becomes $y = \frac{24}{x}$ .

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