1. The problem asks to write equations for three lines given their descriptions and points. 2. For line l (red), it is a horizontal line crossing the y-axis at $y=3$. The equation of a horizontal line is $y = c$, where $c$ is the y-intercept. 3. Therefore, the equation for line l is: $$y = 3$$ 4. For line m (black), it passes through points $(0,6)$ and $(6,0)$. 5. The slope $m$ is calculated by: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{6 - 0} = \frac{-6}{6} = -1$$ 6. Using point-slope form with point $(0,6)$: $$y - 6 = -1(x - 0)$$ 7. Simplify: $$y - 6 = -x$$ $$y = -x + 6$$ 8. For line n (green), it passes through points $(0,-3)$ and $(3,0)$. 9. Calculate the slope: $$m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1$$ 10. Using point-slope form with point $(0,-3)$: $$y - (-3) = 1(x - 0)$$ 11. Simplify: $$y + 3 = x$$ $$y = x - 3$$ Final answers: - Line l: $y = 3$ - Line m: $y = -x + 6$ - Line n: $y = x - 3$