1. The problem asks for equations of lines passing through the point $(2, -5)$ under different conditions. 2. (a) A line with slope $-3$ passing through $(2,-5)$: Use point-slope form: $$y - y_1 = m(x - x_1)$$ where $m = -3$ and $(x_1, y_1) = (2, -5)$. $$y - (-5) = -3(x - 2)$$ Simplify: $$y + 5 = -3x + 6$$ $$y = -3x + 1$$ 3. (b) A line parallel to the x-axis is horizontal, so its slope is 0. The line passing through $(2,-5)$ is: $$y = -5$$ 4. (c) A line parallel to the y-axis is vertical, so its equation is of the form: $$x = c$$ Since it passes through $(2,-5)$, $x=2$. 5. (d) Find the slope of the given line $2x - 4y = 3$: Rearranged to slope-intercept form: $$-4y = -2x + 3$$ $$y = \frac{1}{2}x - \frac{3}{4}$$ So slope $m = \frac{1}{2}$. A parallel line has the same slope $m=\frac{1}{2}$ and passes through $(2,-5)$. Using point-slope form: $$y - (-5) = \frac{1}{2}(x - 2)$$ $$y + 5 = \frac{1}{2}x - 1$$ $$y = \frac{1}{2}x - 6$$ Final answers: (a) $$y = -3x + 1$$ (b) $$y = -5$$ (c) $$x = 2$$ (d) $$y = \frac{1}{2}x - 6$$