Answer
$m= -\dfrac{1}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the slope of the given equation, $
x+3y=-6
,$ convert to the Slope-Intercept Form. Then use a table of values to graph the line.
$\bf{\text{Solution Details:}}$
Using the properties of equality, in the form $y=mx+b,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
3y=-x-6
\\\\
y=-\dfrac{1}{3}x-\dfrac{6}{3}
\\\\
y=-\dfrac{1}{3}x-2
.\end{array}
Using $y=mx+b$ or the Slope-Intercept Form, where $m$ is the slope, then the slope of the equation above is
\begin{array}{l}\require{cancel}
m= -\dfrac{1}{3}
.\end{array}
Graph the equation using the table of values below.