1. **Problem 1:** Find the equation of the line $L$ passing through $(6, -4)$ and parallel to the line $y = 5 - 3x$. 2. The given line can be rewritten in slope-intercept form $y = mx + c$ as: $$y = -3x + 5$$ where the slope $m = -3$. 3. Since $L$ is parallel to this line, it has the same slope $m = -3$. 4. Use the point-slope form of a line equation: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1) = (6, -4)$ and $m = -3$. 5. Substitute values: $$y - (-4) = -3(x - 6)$$ which simplifies to $$y + 4 = -3x + 18$$ 6. Rearranging to slope-intercept form: $$y = -3x + 18 - 4$$ $$y = -3x + 14$$ --- 7. **Problem 2:** Find the midpoint of points $A(4, 1)$ and $B(1, 9)$. 8. The midpoint formula is: $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 9. Substitute the coordinates: $$\left( \frac{4 + 1}{2}, \frac{1 + 9}{2} \right) = \left( \frac{5}{2}, \frac{10}{2} \right)$$ 10. Simplify: $$\left( 2.5, 5 \right)$$ **Final answers:** - Equation of line $L$: $y = -3x + 14$ - Midpoint of $AB$: $(2.5, 5)$