1. **State the problem:** Find the slope $m$ of the line passing through points $P(0,0)$ and $Q(-1, \sqrt{3})$. 2. **Formula for slope:** 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 points:** Here, $P=(0,0)$ and $Q=(-1, \sqrt{3})$, so $$m = \frac{\sqrt{3} - 0}{-1 - 0} = \frac{\sqrt{3}}{-1}$$ 4. **Simplify the fraction:** $$m = \frac{\sqrt{3}}{\cancel{-1}} = -\sqrt{3}$$ 5. **Interpretation:** The slope is negative, meaning the line goes downwards as we move from left to right. **Final answer:** $$m = -\sqrt{3}$$