1. The problem is to find the slope of the line through each pair of points given. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the change in $y$ over the change in $x$. 3. Calculate the slope for each pair: 11) Points $(-2, 10)$ and $(-2, -15)$: $$m = \frac{-15 - 10}{-2 - (-2)} = \frac{-25}{0}$$ Slope is undefined (vertical line). 12) Points $(1, 2)$ and $(-6, -14)$: $$m = \frac{-14 - 2}{-6 - 1} = \frac{-16}{-7} = \frac{16}{7}$$ 13) Points $(-15, 10)$ and $(16, -7)$: $$m = \frac{-7 - 10}{16 - (-15)} = \frac{-17}{31}$$ 14) Points $(13, -2)$ and $(7, 7)$: $$m = \frac{7 - (-2)}{7 - 13} = \frac{9}{-6} = -\frac{3}{2}$$ 15) Points $(10, 18)$ and $(-11, -10)$: $$m = \frac{-10 - 18}{-11 - 10} = \frac{-28}{-21} = \frac{4}{3}$$ 16) Points $(-3, 6)$ and $(-20, 13)$: $$m = \frac{13 - 6}{-20 - (-3)} = \frac{7}{-17} = -\frac{7}{17}$$ 17) Points $(-16, -14)$ and $(11, -14)$: $$m = \frac{-14 - (-14)}{11 - (-16)} = \frac{0}{27} = 0$$ 18) Points $(13, 15)$ and $(2, 10)$: $$m = \frac{10 - 15}{2 - 13} = \frac{-5}{-11} = \frac{5}{11}$$ 19) Points $(-4, 14)$ and $(-16, 8)$: $$m = \frac{8 - 14}{-16 - (-4)} = \frac{-6}{-12} = \frac{1}{2}$$ 20) Points $(9, -6)$ and $(-7, -7)$: $$m = \frac{-7 - (-6)}{-7 - 9} = \frac{-1}{-16} = \frac{1}{16}$$ 21) Points $(12, -19)$ and $(6, 14)$: $$m = \frac{14 - (-19)}{6 - 12} = \frac{33}{-6} = -\frac{11}{2}$$ 22) Points $(-16, 2)$ and $(15, -10)$: $$m = \frac{-10 - 2}{15 - (-16)} = \frac{-12}{31}$$ 23) Points $(-5, -10)$ and $(-5, 20)$: $$m = \frac{20 - (-10)}{-5 - (-5)} = \frac{30}{0}$$ Slope is undefined (vertical line). 24) Points $(8, 11)$ and $(-3, -13)$: $$m = \frac{-13 - 11}{-3 - 8} = \frac{-24}{-11} = \frac{24}{11}$$ 25) Points $(-17, 19)$ and $(10, -7)$: $$m = \frac{-7 - 19}{10 - (-17)} = \frac{-26}{27}$$ 26) Points $(11, -2)$ and $(1, 17)$: $$m = \frac{17 - (-2)}{1 - 11} = \frac{19}{-10} = -\frac{19}{10}$$ 27) Points $(7, -14)$ and $(-8, -9)$: $$m = \frac{-9 - (-14)}{-8 - 7} = \frac{5}{-15} = -\frac{1}{3}$$ 28) Points $(-18, -5)$ and $(14, -3)$: $$m = \frac{-3 - (-5)}{14 - (-18)} = \frac{2}{32} = \frac{1}{16}$$ 29) Points $(-5, 7)$ and $(-18, 14)$: $$m = \frac{14 - 7}{-18 - (-5)} = \frac{7}{-13} = -\frac{7}{13}$$ 30) Points $(19, 15)$ and $(5, 11)$: $$m = \frac{11 - 15}{5 - 19} = \frac{-4}{-14} = \frac{2}{7}$$ Final answers: 11) Undefined 12) $\frac{16}{7}$ 13) $-\frac{17}{31}$ 14) $-\frac{3}{2}$ 15) $\frac{4}{3}$ 16) $-\frac{7}{17}$ 17) $0$ 18) $\frac{5}{11}$ 19) $\frac{1}{2}$ 20) $\frac{1}{16}$ 21) $-\frac{11}{2}$ 22) $-\frac{12}{31}$ 23) Undefined 24) $\frac{24}{11}$ 25) $-\frac{26}{27}$ 26) $-\frac{19}{10}$ 27) $-\frac{1}{3}$ 28) $\frac{1}{16}$ 29) $-\frac{7}{13}$ 30) $\frac{2}{7}$