1. **State the problem:** Find the rate of change (slope) of the linear function passing through points (2, 9) and (-1, 3). 2. **Formula:** The rate of change (slope) $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula:** Using points $(2, 9)$ and $(-1, 3)$: $$m = \frac{3 - 9}{-1 - 2}$$ 4. **Calculate numerator and denominator:** $$m = \frac{-6}{-3}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{-6}}{\cancel{-3}} = 2$$ 6. **Interpretation:** The rate of change of the function is 2, meaning for every 1 unit increase in $x$, $y$ increases by 2 units. **Final answer:** $$\boxed{2}$$