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if y varies inversely as x and y = 4, when x= 2. find y when x=4.
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✏️INVERSE VARIATION

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Problem: If y varies inversely as x and y = 4 when x = 2. Find y when x = 4.

Solution: Make the equation for inverse variation in which k is the constant.

  • [tex] \begin{gathered}y = \frac{k}{x} \end{gathered}[/tex]

  • [tex] \begin{gathered}4 = \frac{k}{2} \end{gathered}[/tex]

  • [tex] \begin{gathered}4 \cdot2= \frac{k}{ \cancel2} \cdot \cancel2 \end{gathered}[/tex]

  • [tex]4 \cdot2 = k[/tex]

  • [tex]k = 8[/tex]

- Find y when x = 4.

  • [tex] \begin{gathered}y = \frac{8}{4} \end{gathered}[/tex]

  • [tex]y = 2[/tex]

- Therefore, the value of y is:

  • [tex] \large \rm Value \: of \: y = \boxed{ \rm \green{ \: \: 2 \: \: }}[/tex]

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