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 \(2 = \frac{2}{3}*(-3) + c\). 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 ：\(\boxed{The equation of the line is y = \frac{2}{3}x + 4}\)