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If $y$ varies inversely with $x$ and $y = 4$ when $x = 3$ , find $y$ when $x = 1$ . $\newline$ 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 = 4

when

x = 3

, find

y

when

x = 1

.

\newline

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

\newline

y =

_____

Understand relationship: Understand the relationship between $y$ and $x$ . Since $y$ varies inversely with $x$ , 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 $y = 4$ when $x = 3$ . Substitute these values into the inverse variation equation to find $k$ . $4 = \frac{k}{3}$ Now, solve for $k$ by multiplying both sides by $3$ . $4 \times 3 = k$ $k = 12$
Write inverse variation equation: Write the inverse variation equation with the found value of $k$ . $\newline$ Now that we have found $k$ to be $12$ , the inverse variation equation is $y = \frac{12}{x}$ .
Find $y$ for $x=1$ : Find $y$ when $x = 1$ using the inverse variation equation. $\newline$ Substitute $x = 1$ into the equation $y = \frac{12}{x}$ . $\newline$ $y = \frac{12}{1}$ $\newline$ $y = 12$

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