Chapter 3 - Equations and Problem Solving - 3.1 - Solving First-Degree Equations - Problem Set 3.1 - Page 100: 56

$y=-\dfrac{4}{9}$

Multiplying both sides by the $LCD= 36 ,$ and using the properties of equality, the value of the variable that satisfies the given equation, $ \dfrac{-y}{4}=\dfrac{1}{9} ,$ is \begin{array}{l}\require{cancel} 9(-y)=4(1) \\\\ -9y=4 \\\\ y=\dfrac{4}{-9} \\\\ y=-\dfrac{4}{9} .\end{array}