Use the given conditions to write an equation for the line in slope-intercept form.
Passing through $(-3,2)$ and parallel to the line whose equation is $y=\frac{2}{3}x+\frac{8}{3}$

Step 1 ：The equation of a line in slope-intercept form is given by $y=mx+c$, where $m$ is the slope and $c$ is the y-intercept.

Step 2 ：A line parallel to another line will have the same slope. Therefore, the slope of the line we are trying to find is $\frac{2}{3}$, the same as the given line.

Step 3 ：We can find the y-intercept by substituting the coordinates of the given point into the equation and solving for $c$. So, we substitute $x=-3$ and $y=2$ into the equation $y=mx+c$ to find the value of $c$.

Step 4 ：Substituting the values we get $2=\frac{2}{3}\ast (-3)+c$. Solving for $c$ we get $c=4$.

Step 5 ：Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form.

Step 6 ：$\boxed{{\displaystyle Theequationofthelineisy=\frac{2}{3}x+4}}$