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Assume that $y$ varies inversely with $x$ . If $y = 1$ 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. Assume that

y

varies inversely with

x

. If

y = 1

when

x = 6

, find

y

when

x = 3

.

\newline

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

\newline

y =

_____

Identify general form: Given that $y$ varies inversely with $x$ . Identify the general form of inverse variation. In inverse variation, variables change in opposite directions. Inverse variation: $y = \frac{k}{x}$
Choose equation with values: We know that $y = 1$ when $x = 6$ . Choose the equation after substituting the values in $y = \frac{k}{x}$ . Substitute $6$ for $x$ and $1$ for $y$ in $y = \frac{k}{x}$ . $1 = \frac{k}{6}$
Solve for k: We found: $\newline$ $1 = \frac{k}{6}$ $\newline$ Solve the equation to find the value of k. $\newline$ To isolate k, multiply both sides by $6$ . $\newline$ $1 \times 6 = \left(\frac{k}{6}\right) \times 6$ $\newline$ $6 = k$
Substitute $k$ in equation: We have: $\newline$ $k = 6$ $\newline$ Write the inverse variation equation in the form of $y = \frac{k}{x}$ . $\newline$ Substitute $k = 6$ in $y = \frac{k}{x}$ . $\newline$ $y = \frac{6}{x}$
Find $y$ for $x=3$ : Inverse variation equation: $\newline$ $y = \frac{6}{x}$ $\newline$ Find $y$ when $x = 3$ . $\newline$ Substitute $3$ for $x$ in $y = \frac{6}{x}$ . $\newline$ $y = \frac{6}{3}$ $\newline$ $y = 2$

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