1. **State the problem:** We are given two points $(-4, r)$ and $(8, 11)$ on a line with slope $\frac{5}{4}$. We need to find the missing coordinate $r$. 2. **Recall the slope formula:** The 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. **Substitute the known values:** Here, $m = \frac{5}{4}$, $x_1 = -4$, $y_1 = r$, $x_2 = 8$, and $y_2 = 11$. So, $$\frac{5}{4} = \frac{11 - r}{8 - (-4)}$$ 4. **Simplify the denominator:** $$8 - (-4) = 8 + 4 = 12$$ So the equation becomes $$\frac{5}{4} = \frac{11 - r}{12}$$ 5. **Cross multiply to solve for $r$:** $$5 \times 12 = 4 \times (11 - r)$$ $$60 = 44 - 4r$$ 6. **Isolate $r$:** $$60 - 44 = -4r$$ $$16 = -4r$$ 7. **Divide both sides by $-4$:** $$\cancel{\frac{16}{-4}} = \cancel{\frac{-4r}{-4}}$$ $$r = -4$$ **Final answer:** $$\boxed{-4}$$