Answer
The $x-$ intercept is $8$.
The graph is shown below.
Work Step by Step
The given equation is
$\Rightarrow x+4y=8$
Subtract $x$ from each side.
$\Rightarrow x+4y-x=8-x$
Simplify.
$\Rightarrow 4y=-x+8$
Divide each side by $4$.
$\Rightarrow \frac{4y}{4}=\frac{-x+8}{4}$
Simplify.
$\Rightarrow y=-\frac{1}{4}x+2$
The slope-intercept form is
$\Rightarrow y=mx+b$
$y-$intercept is $b=2$.
Plot the $y-$ intercept $A=(0,2)$.
The slope is $m=-\frac{1}{4}$ and
Slope $m=\frac{rise}{run}=\frac{-1}{4}$
The next point is $4$ unit right and $1$ unit down from the point $(0,2)$.
Plot the point $B=(4,1)$.
Draw a line through the two points.
From the graph the line crosses the $x-$ axis at $C=(8,0)$.
Hence, the $x-$ intercept is $8$.
