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If $y$ varies inversely with $x$ and $y = 1$ when $x = 6$ , find $y$ when $x = 3$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 1

when

x = 6

, find

y

when

x = 3

.

\newline

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

\newline

y =

_____

Understand Relationship: Understand the relationship between $y$ and $x$ . Inverse variation means that as one variable increases, the other decreases proportionally. The formula for 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 $k$ . We are given that $y = 1$ when $x = 6$ . Substitute these values into the inverse variation formula to find $k$ . $1 = \frac{k}{6}$ Now, solve for $k$ by multiplying both sides by $6$ . $k = 1 \times 6$ $k = 6$
Write Inverse Variation Equation: Write the inverse variation equation with the found constant $k$ . Now that we know $k = 6$ , we can write the equation as $y = \frac{6}{x}$ .
Find $y$ for $x=3$ : Find $y$ when $x = 3$ using the inverse variation equation. $\newline$ Substitute $x = 3$ into the equation $y = \frac{6}{x}$ . $\newline$ $y = \frac{6}{3}$ $\newline$ $y = 2$

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