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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 8$ , find $y$ when $x = 4$ . $\newline$ 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 = 2

when

x = 8

, find

y

when

x = 4

.

\newline

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

\newline

y =

_____

Identify Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We need to find $k$ using the given values.
Substitute Values for $k$ : Substitute $y = 2$ and $x = 8$ into $y = \frac{k}{x}$ to find $k$ . $2 = \frac{k}{8}$
Solve for k: Multiply both sides by $8$ to solve for $k$ . $2 \times 8 = k$
Calculate Constant of Variation: $k = 16$ . Now we have the constant of variation.
Write Inverse Variation Equation: Write the inverse variation equation with $k = 16$ . $y = \frac{16}{x}$
Find $y$ for $x=4$ : Find $y$ when $x = 4$ by substituting $x$ into the equation. $\newline$ $y = \frac{16}{4}$
Final Calculation: Calculate $y$ . $y = 4$ . Oops, we're done here!

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