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Given x varies inversely as y and x = 6 when y = - 4, find y when x = 8 .

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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

Given that x varies inversely with y, x=6 when y=-4, find y when x=8.

[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

If x varies inversely with y, we divide.

So the formula looks as follows:-

[tex]\bold{x=\displaystyle\frac{k}{y} }[/tex]

where k = constant of proportionality

Plug in the values:-

[tex]\bold{6=\displaystyle\frac{k}{-4}}[/tex]

Multiply both sides by -4:-

[tex]\bold{-24=k}[/tex]

Now find y when x=8:-

[tex]\bold{8=\displaystyle\frac{-24}{y}}[/tex]

Multiply both sides by y:-

[tex]\bold{8y=-24}[/tex]

Divide by 8 on both sides:-

[tex]\dashrightarrow\bigstar{\boxed{\boxed{\underline{\bold{y=-3}}}}\dashleftarrow[/tex]

Good luck.

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