1. **Problem statement:** We need to estimate the slope $m$ of the line passing through points $P$ and $Q$ for each pair and classify the slope as either $m \leq 0$ or $m > 0$. 2. **Formula for slope:** The slope $m$ of a line through points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate slopes for each pair:** - A: $P(1,3), Q(4,6)$ $$m = \frac{6 - 3}{4 - 1} = \frac{3}{3} = 1$$ Since $1 > 0$, slope is positive. - B: $P(-1,3), Q(4,-6)$ $$m = \frac{-6 - 3}{4 - (-1)} = \frac{-9}{5} = -1.8$$ Since $-1.8 \leq 0$, slope is non-positive. - C: $P(-1,3), Q(-4,6)$ $$m = \frac{6 - 3}{-4 - (-1)} = \frac{3}{-3} = -1$$ Since $-1 \leq 0$, slope is non-positive. - D: $P(-2,-4), Q(-4,-2)$ $$m = \frac{-2 - (-4)}{-4 - (-2)} = \frac{2}{-2} = -1$$ Since $-1 \leq 0$, slope is non-positive. - E: $P(1,3), Q(3,11)$ $$m = \frac{11 - 3}{3 - 1} = \frac{8}{2} = 4$$ Since $4 > 0$, slope is positive. - F: $P(5,3), Q(4,1)$ $$m = \frac{1 - 3}{4 - 5} = \frac{-2}{-1} = 2$$ Since $2 > 0$, slope is positive. 4. **Classification:** - $m \leq 0$ (red pot): B, C, D - $m > 0$ (yellow pot): A, E, F **Final answer:** - Red pot (non-positive slope): B, C, D - Yellow pot (positive slope): A, E, F