Answer
The $x-$ intercept is $9$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow x+3y=9$
Subtract $x$ from each side.
$\Rightarrow x+3y-x=9-x$
Simplify.
$\Rightarrow 3y=-x+9$
Divide each side by $3$.
$\Rightarrow \frac{3y}{3}=\frac{-x+9}{3}$
Simplify.
$\Rightarrow y=-\frac{1}{3}x+3$
The slope-intercept form is
$\Rightarrow y=mx+b$
$y-$ intercept is $b=3$.
Plot the $y-$ intercept $A=(0,3)$.
The slope is $m=-\frac{1}{3}$.
Slope $m=\frac{rise}{run}=\frac{-1}{3}$
The next point is $3$ unit right and $1$ unit down from the point $(0,3)$.
Plot the point $B=(3,2)$.
Draw a line through the two points.
From the graph the line crosses the $x-$ axis at $C=(9,0)$.
Hence, the $x-$ intercept is $9$.
