Question

Use the given information to find the unknown value:y varies inversely with a. When x = 4, then y= 4. Find y when I = 2.Iyy =help (numbers)

Answer 1

Inverse variation:

$y=\frac{k}{x}$

k is a constant

Use the given information (when x=4 y=4) to find the value of the constant:

$\begin{gathered} 4=\frac{k}{4} \\ \\ \text{Multiply both sides of the equation by 4:} \\ 4\times4=4\times\frac{k}{4} \\ \\ 16=k \\ \\ \\ k=16 \end{gathered}$

Then, the given relationship has the next equation:

$y=\frac{16}{x}$

Use the equation above to find y when x=2:

$\begin{gathered} y=\frac{16}{2} \\ \\ y=8 \end{gathered}$Then, when x=2, y=8