1. **Solve the equation** $y - 12x + 3 = \frac{4}{7}$ for $y$. Start by isolating $y$ on one side: $$y = 12x - 3 + \frac{4}{7}$$ Convert $-3$ to a fraction with denominator 7: $$-3 = -\frac{21}{7}$$ So, $$y = 12x - \frac{21}{7} + \frac{4}{7} = 12x - \frac{21 - 4}{7} = 12x - \frac{17}{7}$$ 2. **Find the equation of the line passing through points $(5,9)$ and $(0,-2)$ in the form $y = mx + b$**. Calculate the slope $m$: $$m = \frac{9 - (-2)}{5 - 0} = \frac{11}{5}$$ Use point-slope form with point $(0,-2)$: $$y - (-2) = \frac{11}{5}(x - 0)$$ $$y + 2 = \frac{11}{5}x$$ Isolate $y$: $$y = \frac{11}{5}x - 2$$ 3. **Write an equation for the monkey's depth $y$ after time $x$ minutes, starting at $-14$ meters and climbing at $\frac{7}{3}$ meters per minute**. The depth decreases as the monkey climbs, so the rate is positive upward. The equation is: $$y = -14 + \frac{7}{3}x$$ **Final answers:** (A) $$y = 12x - \frac{17}{7}$$ (B) $$y = \frac{11}{5}x - 2$$ (C) $$y = -14 + \frac{7}{3}x$$