1. **State the problem:** Find the equation of the line passing through the points $(-3,0)$ and $(0,2)$ in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ The slope-intercept form is: $$y=mx+b$$ where $b$ is the $y$-intercept. 3. **Calculate the slope:** $$m=\frac{2 - 0}{0 - (-3)}=\frac{2}{3}$$ 4. **Find the $y$-intercept $b$:** Since the line passes through $(0,2)$, the $y$-intercept is $b=2$. 5. **Write the equation:** $$y=\frac{2}{3}x + 2$$ **Final answer:** The equation of the line in slope-intercept form is $y=\frac{2}{3}x + 2$.