1. **State the problem:** We are given three points A(2,5), B(9,-2), and J(4,h) that lie on the same straight line. We need to find the value of $h$. 2. **Find the slope of the line passing through points A and B:** $$\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 5}{9 - 2} = \frac{-7}{7} = -1$$ 3. **Use the slope to find $h$ for point J(4,h):** Since J lies on the same line, the slope between A and J must also be $-1$. Calculate slope between A and J: $$m = \frac{h - 5}{4 - 2} = \frac{h - 5}{2}$$ Set equal to $-1$: $$\frac{h - 5}{2} = -1$$ 4. **Solve for $h$:** $$h - 5 = -2$$ $$h = 3$$ 5. **Conclusion:** The value of $h$ is 3, which corresponds to option C.