1. **Calculate the slope of each line segment, where possible.** The slope formula for a line segment between points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}$$ Important rules: - If $x_2 = x_1$, the slope is undefined (vertical line). - If $y_2 = y_1$, the slope is zero (horizontal line). --- **a) AB:** Points $A(2,2)$ and $B(4,3)$ $$m = \frac{3 - 2}{4 - 2} = \frac{1}{2}$$ **b) CD:** Points $C(-1,2)$ and $D(2,4)$ $$m = \frac{4 - 2}{2 - (-1)} = \frac{2}{3}$$ **c) EF:** Points $E(0,-2)$ and $F(1,-6)$ $$m = \frac{-6 - (-2)}{1 - 0} = \frac{-4}{1} = -4$$ **d) GH:** Horizontal line segment at $y=6$ from $x=-3$ to $x=2$ Since $y$ is constant, slope: $$m = 0$$ **e) IJ:** Vertical line segment at $x=-4$ from $y=2$ to $y=-4$ Since $x$ is constant, slope is undefined. **f) KL:** Points $K(2,-2)$ and $L(4,-1)$ $$m = \frac{-1 - (-2)}{4 - 2} = \frac{1}{2}$$ --- 2. **Calculate the slope of the following lines (graphs shown):** - Bottom left graph: Line crosses y-axis near $-3$ and x-axis near $3$. Slope formula using intercepts $(0,-3)$ and $(3,0)$: $$m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1$$ - Bottom right graph: Line crosses y-axis near $4$ and x-axis near $-2$. Slope formula using intercepts $(0,4)$ and $(-2,0)$: $$m = \frac{0 - 4}{-2 - 0} = \frac{-4}{-2} = 2$$ --- **Final answers:** - a) $\frac{1}{2}$ - b) $\frac{2}{3}$ - c) $-4$ - d) $0$ - e) undefined - f) $\frac{1}{2}$ - Bottom left line: $1$ - Bottom right line: $2$