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Assume that $y$ varies inversely with $x$ . If $y = -4$ when $x = 8$ , 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 = -4

when

x = 8

, find

y

when

x = 2

.

\newline

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

\newline

y =

_____

Find k value: Given $y = -4$ when $x = 8$ , plug these values into the inverse variation formula to find $k$ . $-4 = \frac{k}{8}$ Multiply both sides by $8$ to solve for $k$ . $-4 \times 8 = k$ $k = -32$
Calculate inverse variation equation: Now we have the inverse variation equation $y = \frac{-32}{x}$ . $\newline$ We need to find $y$ when $x = 2$ . $\newline$ Substitute $x = 2$ into the equation. $\newline$ $y = \frac{-32}{2}$ $\newline$ $y = -16$

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