Answer
$y=-\dfrac{3}{2}x-8$
Work Step by Step
Using $y=mx+b$, where $m$ is the slope, the slope of the given line, $
y=-\dfrac{3}{2}x+11
$ is
\begin{array}{l}
m=-\dfrac{3}{2}
.\end{array}
Using $m=
-\dfrac{3}{2}
$ (parallel lines have same slope) and the given point $(
-6,1
),$ then the equation of the line is
\begin{array}{l}
y-1=-\dfrac{3}{2}(x-(-6))
\\\\
y-1=-\dfrac{3}{2}(x+6)
\\\\
y-1=-\dfrac{3}{2}x-9
\\\\
y=-\dfrac{3}{2}x-9+1
\\\\
y=-\dfrac{3}{2}x-8
.\end{array}
