Answer
The $x-$ intercept is $-\frac{1}{3}$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow 3x+y=-1$
Subtract $3x$ from each side.
$\Rightarrow 3x+y-3x=-1-3x$
Simplify.
$\Rightarrow y=-3x-1$
The slope-intercept form is
$\Rightarrow y=mx+b$
$y-$intercept is $b=-1$.
Plot the $y-$ intercept $A=(0,-1)$.
The slope is $m=-3$ and
Slope $m=\frac{rise}{run}=\frac{-3}{1}$
The next point is $1$ unit right and $3$ unit down from the point $(0,-1)$.
Plot the point $B=(1,-4)$.
Draw a line through the two points.
From the graph the line crosses the $x-$ axis at $C=(-\frac{1}{3},0)$.
Hence, the $x-$ intercept is $-\frac{1}{3}$.
