Answer
The $y$-intercept is $2$.
The slope is $m=\frac{1}{3}$.
See the graph below.
Work Step by Step
First, we have to get the equation's slope-intercept form, that is $y=mx+b$:
Add $x$ to both sides of the equation, then divide both sides by $3$ to obtain:
\begin{align*}
-x+3y+x&=6+x\\
3y&=x+6\\
\frac{3y}{3}&=\frac{x+6}{3}\\
y&=\frac{1}{3}x+2\end{align*}
This form of the equation is the slope-intercept form.
In this form, the slope of the line equals to the coefficient of $x$ (which is $m$) and the $y$-intercept equals to the constant $b$.
Therefore in the equation $y=\dfrac{1}{3}x+2$:
The $y$-intercept is $2$.
The slope is $\dfrac{1}{3}$.
In order to graph the line, we have to sketch the $y$-intercept, that is $(0,2)$.
As the slope is $\frac{1}{3}$, we can find another point that we can also sketch.
The slope is the change in $y$ for every $1$ unit change of $x$.
Thus, a slope of $\frac{1}{3}$ means a $1$-unit increase in $x$ will result to a $\frac{1}{3}$-unit increase in $y$. This is equivalent to a $1$ unit increase in $y$ for a $3$-unit increase in $x$.
Using $(0,2)$ as the starting point and a slope of $\frac{1}{3}$, the coordinates of another point on the line would be:
$(0+3, 2+1)=(3,3)$
Plot the two points then connect them using a straigiht line.
Refer to the graph above,
