1. **State the problem:** We need to find the equation of a line passing through the point $(-10, 12)$ with slope $m = -\frac{9}{5}$. The equation should be in standard form $Ax + By = C$. 2. **Use the point-slope form:** The point-slope form of a line is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the given point and slope:** $$y - 12 = -\frac{9}{5}(x - (-10))$$ which simplifies to $$y - 12 = -\frac{9}{5}(x + 10)$$ 4. **Distribute the slope:** $$y - 12 = -\frac{9}{5}x - \frac{9}{5} \times 10$$ $$y - 12 = -\frac{9}{5}x - 18$$ 5. **Add 12 to both sides:** $$y = -\frac{9}{5}x - 18 + 12$$ $$y = -\frac{9}{5}x - 6$$ 6. **Rewrite in standard form $Ax + By = C$:** Move all terms to one side: $$\frac{9}{5}x + y = -6$$ 7. **Clear the fraction by multiplying both sides by 5:** $$5 \times \left(\frac{9}{5}x + y\right) = 5 \times (-6)$$ $$\cancel{5} \times \left(\frac{9}{\cancel{5}}x\right) + 5y = -30$$ $$9x + 5y = -30$$ 8. **Check the options:** The equation $\frac{9}{5}x + y = -6$ matches one of the given options exactly (third option). This is the standard form with fractions. **Final answer:** $$\frac{9}{5}x + y = -6$$