Answer
$x-$ intercept is $6$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow x+2y=6$
Subtract $x$ from each side.
$\Rightarrow x+2y-x=6-x$
Simplify.
$\Rightarrow 2y=-x+6$
Divide each side by $2$.
$\Rightarrow \frac{2y}{2}=\frac{-x+6}{2}$
Simplify.
$\Rightarrow y=-\frac{1}{2}x+3$
The slope-intercept form is
$\Rightarrow y=mx+b$
$y-$intercept is $b=3$.
Plot the $y-$ intercept $A=(0,3)$.
The slope is $m=-\frac{1}{2}$ and
Slope $m=\frac{rise}{run}=\frac{-1}{2}$
The next point is $2$ unit right and $1$ unit down from the point $(0,3)$.
Plot the point $B=(2,2)$.
Draw a line through the two points.
From the graph the line crosses the $x-$ axis at $C=(6,0)$.
Hence, the $x-$ intercept is $6$.
