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Assume that $y$ varies inversely with $x$ . If $y = 1$ when $x = 6$ , find $y$ when $x = 2$ . $\newline$ 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. Assume that

y

varies inversely with

x

. If

y = 1

when

x = 6

, find

y

when

x = 2

.

\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. The relationship can be described by the equation $y = \frac{k}{x}$ , 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 equation to find $k$ . $1 = \frac{k}{6}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $6$ . $\newline$ $1 \times 6 = \left(\frac{k}{6}\right) \times 6$ $\newline$ $6 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we know $k = 6$ , we can write the equation as $y = \frac{6}{x}$ .
Find y: Find $y$ when $x = 2$ . $\newline$ Substitute $2$ for $x$ in the equation $y = \frac{6}{x}$ . $\newline$ $y = \frac{6}{2}$ $\newline$ $y = 3$

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