Answer
The $x-$intercept is $(4,\,\,0)$.
The $y-$intercept is $(0,\,6)$.
The graph of the line is as shown below:
Work Step by Step
To find the $x-$intercept, substitute $y=0$ in the equation$\frac{1}{2}x+\frac{1}{3}y=2$.
$\Rightarrow \frac{1}{2}x+\frac{1}{3}\left( 0 \right)=2$
$\Rightarrow \frac{1}{2}x=2$
Multiply on both sides by $2$,
$\Rightarrow x=4$
The $x-$intercept is $4$, and the point $\left( 4,0 \right)$ is on the graph of the equation.
To find the $y-$intercept, substitute $x=0$ in the equation $\frac{1}{2}x+\frac{1}{3}y=2$.
$\Rightarrow \frac{1}{2}\left( 0 \right)+\frac{1}{3}y=2$
$\Rightarrow \frac{1}{3}y=2$
Multiply on both sides by $3$,
$\Rightarrow y=6$
The $y-$intercept is $6$, and the point $\left( 0,6 \right)$ is on the graph of the equation.
To draw the graph, plot the two intercepts and connect them with a line.
