Chapter 8 - Coordinate Geometry and Linear Systems - 8.4 - Writing Equations of Lines - Problem Set 8.4 - Page 360: 6

$5x+6y=-34$

Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with the given point $( -2,-4 )$ and slope $m= -\dfrac{5}{6} $ is \begin{array}{l}\require{cancel} y-(-4)=-\dfrac{5}{6}(x-(-2)) \\\\ y+4=-\dfrac{5}{6}(x+2) \\\\ 6(y+4)=-5(x+2) \\\\ 6y+24=-5x-10 \\\\ 5x+6y=-10-24 \\\\ 5x+6y=-34 .\end{array}