Chapter 8 - Coordinate Geometry and Linear Systems - 8.4 - Writing Equations of Lines - Problem Set 8.4 - Page 360: 9

$4x+9y=0$

Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with the given point $( 0,0 )$ and slope $m= -\dfrac{4}{9} $ is \begin{array}{l}\require{cancel} y-0=-\dfrac{4}{9}(x-0) \\\\ y=-\dfrac{4}{9}x \\\\ 9y=-4x \\\\ 4x+9y=0 .\end{array}