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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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