1. **Problem statement:** Determine the slope of each line given the descriptions. 2. **Recall the slope formula:** For two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Important rules:** - A vertical line has an undefined slope because $x_2 - x_1=0$ causes division by zero. - A horizontal line has slope $0$ because $y_2 - y_1=0$. 4. **Calculate slopes:** **a)** Vertical line passing through $x=2$. - Slope is undefined. **b)** Line through points $(0,3)$ and $(3,0)$: $$m=\frac{0 - 3}{3 - 0}=\frac{-3}{3}=-1$$ **c)** Horizontal line passing through $y=-2$. - Slope is $0$. **d)** Line through points $(0,-1)$ and $(2,2)$: $$m=\frac{2 - (-1)}{2 - 0}=\frac{3}{2}$$ 5. **Final answers:** - a) slope is undefined - b) slope is $-1$ - c) slope is $0$ - d) slope is $\frac{3}{2}$