1. **State the problem:** We are given two lines defined by points and need to find their slopes and determine their relationship (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. **Find slope of Line 1:** Points are $(3, 1)$ and $(6, -5)$. $$m_1 = \frac{-5 - 1}{6 - 3} = \frac{-6}{3} = -2$$ 4. **Find slope of Line 2:** Points are $(-7, 10)$ and $(-5, 6)$. $$m_2 = \frac{6 - 10}{-5 - (-7)} = \frac{-4}{2} = -2$$ 5. **Compare slopes:** Both slopes are $-2$. - Lines are **parallel** if their slopes are equal. - Lines are **perpendicular** if the product of their slopes is $-1$. 6. Since $m_1 = m_2 = -2$, the lines are **parallel**. **Final answers:** - a) Slope of Line 1 is $-2$. - b) Slope of Line 2 is $-2$. - c) Lines are parallel.