1. The problem is to find linear equations that pass through the points where the stars are located: (2,8), (2,4), (8,7), and (14,4). 2. Recall that a linear equation in two variables $x$ and $y$ can be written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. First, observe the points (2,8) and (2,4). Both have the same $x$-coordinate, so the line passing through them is vertical: $x = 2$. 4. Next, consider the points (2,4) and (14,4). Both have the same $y$-coordinate, so the line passing through them is horizontal: $y = 4$. 5. Now, find the equation of the line passing through (2,8) and (8,7). Calculate the slope: $$m = \frac{7 - 8}{8 - 2} = \frac{-1}{6} = -\frac{1}{6}$$ 6. Use point-slope form with point (2,8): $$y - 8 = -\frac{1}{6}(x - 2)$$ 7. Simplify: $$y - 8 = -\frac{1}{6}x + \frac{2}{6}$$ $$y = -\frac{1}{6}x + \frac{1}{3} + 8$$ $$y = -\frac{1}{6}x + \frac{25}{3}$$ 8. Finally, find the equation of the line passing through (8,7) and (14,4). Calculate the slope: $$m = \frac{4 - 7}{14 - 8} = \frac{-3}{6} = -\frac{1}{2}$$ 9. Use point-slope form with point (8,7): $$y - 7 = -\frac{1}{2}(x - 8)$$ 10. Simplify: $$y - 7 = -\frac{1}{2}x + 4$$ $$y = -\frac{1}{2}x + 11$$ Summary of linear equations that collect all stars: - $x = 2$ - $y = 4$ - $y = -\frac{1}{6}x + \frac{25}{3}$ - $y = -\frac{1}{2}x + 11$