1. **State the problem:** We need to find the slopes of two lines given two points on each line and then determine if the lines are parallel, perpendicular, or neither. 2. **Formula for slope:** The slope $m$ of a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate slope of Line 1:** Points are $(10,9)$ and $(0,3)$. $$m_1 = \frac{3 - 9}{0 - 10} = \frac{-6}{-10}$$ 4. **Simplify slope of Line 1:** $$m_1 = \frac{\cancel{-6}}{\cancel{-10}} = \frac{6}{10} = \frac{3}{5}$$ 5. **Calculate slope of Line 2:** Points are $(-10,-4)$ and $(0,2)$. $$m_2 = \frac{2 - (-4)}{0 - (-10)} = \frac{2 + 4}{0 + 10} = \frac{6}{10}$$ 6. **Simplify slope of Line 2:** $$m_2 = \frac{\cancel{6}}{\cancel{10}} = \frac{3}{5}$$ 7. **Compare slopes:** Since $m_1 = m_2 = \frac{3}{5}$, the lines have the same slope. 8. **Conclusion:** Lines with the same slope are parallel. **Final answer:** - Slope of Line 1 is $\frac{3}{5}$. - Slope of Line 2 is $\frac{3}{5}$. - Line 1 is parallel to Line 2.