1. **State the problem:** Find the equations of two parallel lines given points on each line. 2. **Formula and rules:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Find the slope of the first line:** Using points $(-2,1)$ and $(0,6)$, $$m = \frac{6 - 1}{0 - (-2)} = \frac{5}{2}$$ 4. **Find the y-intercept of the first line:** Using point $(0,6)$, $$b = 6$$ 5. **Equation of the first line:** $$y = \frac{5}{2}x + 6$$ 6. **Find the slope of the second line:** Using points $(-2,-3)$ and $(0,2)$, $$m = \frac{2 - (-3)}{0 - (-2)} = \frac{5}{2}$$ 7. **Find the y-intercept of the second line:** Using point $(0,2)$, $$b = 2$$ 8. **Equation of the second line:** $$y = \frac{5}{2}x + 2$$ 9. **Conclusion:** Both lines have slope $\frac{5}{2}$ and different y-intercepts, confirming they are parallel. **Final answers:** $$y = \frac{5}{2}x + 6$$ $$y = \frac{5}{2}x + 2$$