Answer
$2x+y=-2$
Work Step by Step
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}
