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Assume that $y$ varies inversely with $x$ . If $y = 1$ when $x = 4$ , 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 = 4

, find

y

when

x = 2

.

\newline

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

\newline

y =

_____

Define Inverse Variation: Inverse variation means $y = \frac{k}{x}$ , where $k$ is a constant. We need to find $k$ using the given values.
Substitute Values: Substitute $y = 1$ and $x = 4$ into the equation to find $k$ : $1 = \frac{k}{4}$ .
Solve for Constant: Multiply both sides by $4$ to solve for $k$ : $4 \times 1 = k$ .
Final Equation: So, $k = 4$ . Now we have the equation $y = \frac{4}{x}$ .
Find $y$ : Substitute $x = 2$ into the equation to find $y$ : $y = \frac{4}{2}$ .
Calculate y: Calculate y: $y = 2$ .

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