Chapter 8 - Coordinate Geometry and Linear Systems - 8.4 - Writing Equations of Lines - Problem Set 8.4 - Page 360: 4

$3x-5y=45$

Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with the given point $( 5,-6 )$ and slope $m= \dfrac{3}{5} $ is \begin{array}{l}\require{cancel} y-(-6)=\dfrac{3}{5}(x-5) \\\\ y+6=\dfrac{3}{5}(x-5) \\\\ 5(y+6)=3(x-5) \\\\ 5y+30=3x-15 \\\\ -3x+5y=-15-30 \\\\ -3x+5y=-45 \\\\ 3x-5y=45 .\end{array}