1. **State the problem:** Write the equation of the line passing through the points $(14, 92)$ and $(17, 76)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** $$m = \frac{76 - 92}{17 - 14} = \frac{-16}{3}$$ 4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1)$$ Using point $(14, 92)$: $$y - 92 = -\frac{16}{3}(x - 14)$$ 5. **Simplify the equation:** $$y - 92 = -\frac{16}{3}x + \frac{16}{3} \times 14$$ $$y - 92 = -\frac{16}{3}x + \frac{224}{3}$$ 6. **Add 92 to both sides:** $$y = -\frac{16}{3}x + \frac{224}{3} + 92$$ 7. **Convert 92 to fraction:** $$92 = \frac{276}{3}$$ 8. **Combine constants:** $$y = -\frac{16}{3}x + \frac{224}{3} + \frac{276}{3} = -\frac{16}{3}x + \frac{500}{3}$$ **Final answer:** $$\boxed{y = -\frac{16}{3}x + \frac{500}{3}}$$