Question

If y is inversely proportional to x and y = -97 when x = 32, find y if x = 13. (Round off youranswer to the nearest hundredth.)

Answer 1

Recall that when y is inversely proportional to x, then

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

Given that y = -97 when x = 32, solve for k

$\begin{gathered} y=\frac{k}{x} \\ -97=\frac{k}{32} \\ -97\cdot32=k \\ -3104=k \\ k=-3104 \end{gathered}$

Next, solve for y when k = -3104, and x = 13.

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{-3104}{13} \\ y=-238.76923 \end{gathered}$

Rounding to the nearest hundredth, if x = 13, then y = -238.77.