Question

#1 (-6,-17) and (-1,-2)
#3 (-7,6) and (-5,2)
#5 (8,-1) and (5,-16)
#7 (3,-1) and (-1,0)
#9 (-2,9) and (10,-1)
#11 (-5,-10) and (-10,10)
#13 (-5,7) and (-1,3)
#15 (5,10) and (12,-11)
#17 (-11,-2) and (-1,2)
#19 (-16,2) and (0,-10)
#21 (-1,8) and (-2,8)
#2 (-16,15) and (4,3)
#4 (-11,-10) and (-20,2)
#6 (-5,6) and (-2,9)
#8 (2,10) and (2,-5) m=undefined
#10 (9,-20) and (11,2)
#12 (13,-8) and (-5,-17)
#14 (9,9) and (-11,13)
#16 (-7,8) and (-8,-1)
#18 (-8,-6) and (-10,4)
#20 (6,4) and (1,0)
#22 (-6,-11) and (18,-19)

Explanation:

Step1: Recall slope - formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Solve for #1

For points $(-6,-17)$ and $(-1,-2)$, $x_1=-6,y_1 = - 17,x_2=-1,y_2=-2$. Then $m=\frac{-2-(-17)}{-1-(-6)}=\frac{-2 + 17}{-1 + 6}=\frac{15}{5}=3$.

Step3: Solve for #2

For points $(-16,15)$ and $(4,3)$, $x_1=-16,y_1 = 15,x_2=4,y_2=3$. Then $m=\frac{3 - 15}{4-(-16)}=\frac{-12}{4 + 16}=-\frac{12}{20}=-\frac{3}{5}$.

Step4: Solve for #3

For points $(-7,6)$ and $(-5,2)$, $x_1=-7,y_1 = 6,x_2=-5,y_2=2$. Then $m=\frac{2 - 6}{-5-(-7)}=\frac{-4}{-5 + 7}=\frac{-4}{2}=-2$.

Step5: Solve for #4

For points $(-11,-10)$ and $(-20,2)$, $x_1=-11,y_1=-10,x_2=-20,y_2 = 2$. Then $m=\frac{2-(-10)}{-20-(-11)}=\frac{2 + 10}{-20 + 11}=\frac{12}{-9}=-\frac{4}{3}$.

Step6: Solve for #5

For points $(8,-1)$ and $(5,-16)$, $x_1=8,y_1=-1,x_2=5,y_2=-16$. Then $m=\frac{-16-(-1)}{5 - 8}=\frac{-16 + 1}{5 - 8}=\frac{-15}{-3}=5$.

Step7: Solve for #6

For points $(-5,6)$ and $(-2,9)$, $x_1=-5,y_1 = 6,x_2=-2,y_2=9$. Then $m=\frac{9 - 6}{-2-(-5)}=\frac{3}{-2 + 5}=\frac{3}{3}=1$.

Step8: Solve for #7

For points $(3,-1)$ and $(-1,0)$, $x_1=3,y_1=-1,x_2=-1,y_2=0$. Then $m=\frac{0-(-1)}{-1 - 3}=\frac{0 + 1}{-1 - 3}=-\frac{1}{4}$.

Step9: Solve for #9

For points $(-2,9)$ and $(10,-1)$, $x_1=-2,y_1 = 9,x_2=10,y_2=-1$. Then $m=\frac{-1 - 9}{10-(-2)}=\frac{-10}{10 + 2}=-\frac{5}{6}$.

Step10: Solve for #10

For points $(9,-20)$ and $(11,2)$, $x_1=9,y_1=-20,x_2=11,y_2=2$. Then $m=\frac{2-(-20)}{11 - 9}=\frac{2 + 20}{11 - 9}=\frac{22}{2}=11$.

Step11: Solve for #11

For points $(-5,-10)$ and $(-10,10)$, $x_1=-5,y_1=-10,x_2=-10,y_2 = 10$. Then $m=\frac{10-(-10)}{-10-(-5)}=\frac{10 + 10}{-10 + 5}=\frac{20}{-5}=-4$.

Step12: Solve for #12

For points $(13,-8)$ and $(-5,-17)$, $x_1=13,y_1=-8,x_2=-5,y_2=-17$. Then $m=\frac{-17-(-8)}{-5 - 13}=\frac{-17 + 8}{-5 - 13}=\frac{-9}{-18}=\frac{1}{2}$.

Step13: Solve for #13

For points $(-5,7)$ and $(-1,3)$, $x_1=-5,y_1 = 7,x_2=-1,y_2=3$. Then $m=\frac{3 - 7}{-1-(-5)}=\frac{-4}{-1 + 5}=\frac{-4}{4}=-1$.

Step14: Solve for #14

For points $(9,9)$ and $(-11,13)$, $x_1=9,y_1 = 9,x_2=-11,y_2=13$. Then $m=\frac{13 - 9}{-11 - 9}=\frac{4}{-20}=-\frac{1}{5}$.

Step15: Solve for #15

For points $(5,10)$ and $(12,-11)$, $x_1=5,y_1 = 10,x_2=12,y_2=-11$. Then $m=\frac{-11 - 10}{12 - 5}=\frac{-21}{7}=-3$.

Step16: Solve for #16

For points $(-7,8)$ and $(-8,-1)$, $x_1=-7,y_1 = 8,x_2=-8,y_2=-1$. Then $m=\frac{-1 - 8}{-8-(-7)}=\frac{-9}{-8 + 7}=9$.

Step17: Solve for #17

For points $(-11,-2)$ and $(-1,2)$, $x_1=-11,y_1=-2,x_2=-1,y_2 = 2$. Then $m=\frac{2-(-2)}{-1-(-11)}=\frac{2 + 2}{-1 + 11}=\frac{4}{10}=\frac{2}{5}$.

Step18: Solve for #18

For points $(-8,-6)$ and $(-10,4)$, $x_1=-8,y_1=-6,x_2=-10,y_2 = 4$. Then $m=\frac{4-(-6)}{-10-(-8)}=\frac{4 + 6}{-10 + 8}=\frac{10}{-2}=-5$.

Step19: Solve for #19

For points $(-16,2)$ and $(0,-10)$, $x_1=-16,y_1 = 2,x_2=0,y_2=-10$. Then $m=\frac{-10 - 2}{0-(-16)}=\frac{-12}{0 + 16}=-\frac{3}{4}$.

Step20: Solve for #20

For points $(6,4)$ and $(1,0)$, $x_1=6,y_1 = 4,x_2=1,y_2=0$. Then $m=\frac{0 - 4}{1 - 6}=\frac{-4}{-5}=\frac{4}{5}$.

Step21: Solve for #21

For points $(-1,8)$ and $(-2,8)$, $x_1=-1,y_1 = 8,x_2=-2,y_2=8$. Then $m=\frac{8 - 8}{-2-(-1)}=\frac{0}{-2 + 1}=0$.

Step22: Solve for #22

For points $(-6,-11)$ and $(18,-19)$, $x_1=-6,y_1=-11,x_2=18,y_2=-19$. Then $m=\frac{-19-(-11)}{18-(-6)}=\frac{-19 + 11}{18 + 6}=\frac{-8}{24}=-\frac{1}{3}$.

Answer:

#1: 3
#2: $-\frac{3}{5}$
#3: -2
#4: $-\frac{4}{3}$
#5: 5
#6: 1
#7: $-\frac{1}{4}$
#9: $-\frac{5}{6}$
#10: 11
#11: -4
#12: $\frac{1}{2}$
#13: -1
#14: $-\frac{1}{5}$
#15: -3
#16: 9
#17: $\frac{2}{5}$
#18: -5
#19: $-\frac{3}{4}$
#20: $\frac{4}{5}$
#21: 0
#22: $-\frac{1}{3}$