Respuesta :
When we have the statement " y varies inversely as x ". We have the next equation:
[tex]y=\frac{k}{x}[/tex]Where k represents the constant between them.
Replace using the given values:
y=2
x=8
[tex]2=\frac{k}{8}[/tex]Now, solve for k:
Multiply both sides by 8
[tex]\begin{gathered} 8\cdot2=8\cdot\frac{k}{8} \\ 16=k \end{gathered}[/tex]Hence, the constant value k is equal to 16.
Let's find x where y=14 and k =16.
Use the same equation to find x and replace it with the given values:
[tex]\begin{gathered} 14=\frac{16}{x} \\ \text{Multiply both sides by x} \\ x\cdot14=x\cdot\frac{16}{x} \\ \text{Simplify} \\ 14x=16 \\ \text{Now, divide both sides by 14} \end{gathered}[/tex][tex]\begin{gathered} \frac{14}{14}x=\frac{16}{14} \\ x=\frac{8}{7} \end{gathered}[/tex]Hence, when y=14, the x value will be 8/7
