## Intermediate Algebra (6th Edition)

$2x+y=-2$
Using the properties of equality, the given equation, $6x+3y=5 ,$ is equivalent to \begin{array}{l} 3y=-6x+5 \\\\ y=-\dfrac{6}{3}x+\dfrac{5}{3} \\\\ y=-2x+\dfrac{5}{3} .\end{array} Using $y=mx+b$, where $m$ is the slope, the slope is \begin{array}{l} m=-2 .\end{array} Using the same slope (since the lines are parallel) and the given point $( 2,-6 ),$ then the equation of the line is \begin{array}{l} y-(-6)=-2(x-2) \\\\ y+6=-2x+4 \\\\ 2x+y=4-6 \\\\ 2x+y=-2 .\end{array}