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If $y$ varies inversely with $x$ and $y = -5$ when $x = 15$ , 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. If

y

varies inversely with

x

and

y = -5

when

x = 15

, find

y

when

x = -3

.

\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 $y = -5$ when $x = 15$ .
Plug in Values: Plug in the values: $-5 = \frac{k}{15}$ . Now solve for $k$ by multiplying both sides by $15$ .
Solve for k: $–5 \times 15 = k$ . So, $k = –75$ .
Finalize Equation: Now we have the inverse variation equation: $y = \frac{-75}{x}$ . Let's find $y$ when $x = -3$ .
Substitute $x$ : Substitute $–3$ for $x$ : $y = \frac{–75}{–3}$ .
Calculate $y$ : Calculate $y$ : $y = 25$ . Oops, that's not right, I divided wrong.

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