1. **State the problem:** Find the slope of the line segment connecting the points $(a,b)$ and $(-a,b)$. Interpret the meaning of the slope. 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 given points:** Here, $x_1 = a$, $y_1 = b$, $x_2 = -a$, and $y_2 = b$. So, $$m = \frac{b - b}{-a - a} = \frac{0}{-2a}$$ 4. **Simplify the expression:** $$m = 0$$ 5. **Interpretation:** A slope of zero means the line segment is horizontal. This means the $y$-values do not change as $x$ changes, so the line is flat. **Final answer:** The slope of the line segment connecting $(a,b)$ and $(-a,b)$ is $0$, indicating a horizontal line segment.