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In an inverse variation, x=2 when y=-4.
What is the value of y when x=16 ?

In an inverse variation, $x=2$ when $y=-4$ . $\newline$ What is the value of $y$ when $x=16$ ?

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Write and solve inverse variation equations

Full solution

Q. In an inverse variation,

x=2

when

y=-4

.

\newline

What is the value of

y

when

x=16

?

Identify Inverse Variation: Given that $y$ varies inversely with $x$ , we use the general form of inverse variation. $\newline$ Inverse variation: $y = \frac{k}{x}$
Find Constant of Variation: We know that $y = -4$ when $x = 2$ . Substitute $2$ for $x$ and $-4$ for $y$ in $y = \frac{k}{x}$ to find the constant of variation $k$ . $-4 = \frac{k}{2}$
Calculate Value of k: Solve the equation to find the value of $k$ . $\newline$ Multiply both sides by $2$ to isolate $k$ . $\newline$ $-4 \times 2 = (k / 2) \times 2$ $\newline$ $-8 = k$
Write Inverse Variation Equation: Now that we have $k = -8$ , we can write the inverse variation equation. $\newline$ Substitute $k = -8$ into $y = \frac{k}{x}$ . $\newline$ $y = \frac{-8}{x}$
Substitute $x = 16$ : To find $y$ when $x = 16$ , substitute $16$ for $x$ in $y = -\frac{8}{x}$ . $\newline$ $y = -\frac{8}{16}$ $\newline$ $y = -\frac{1}{2}$

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