Question

find the slope of the line that passes through each pair of points. 11. (4,3),(-1,6) 12. (8, - 2),(1,1) 13. (2,2),(-2,-2) 14. (6, - 10),(6,14) 15. (5, - 4),(9, - 4) 16. (11,7),(-6,2) 17. (-3,5),(3,6) 18. (-3,2),(7,2) 19. (8,10),(-4,-6) 20. (-12,15),(18, - 13) 21. (-8,6),(-8,4) 22. (-8,-15),(-2,5) 23. (2,5),(3,6) 24. (6,1),(-6,1) 25. (4,6),(4,8) 26. (-5,-8),(-8,1) 27. (2,5),(-3,-5) 28. (9,8),(7,-8) 29. (5,2),(5, - 2) 30. (10,0),(-2,4) 31. (17,18),(18,17) 32. (-6,-4),(4,1) 33. (-3,10),(-3,7) 34. (2,-1),(-8,-2) 35. (5, - 9),(3, - 2) 36. (12,6),(3, - 5) 37. (-4,5),(-8,-5)

Explanation:

Step1: Recall slope formula

The slope $m$ of a line passing through 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: For example, for points $(8,-2)$ and $(1,1)$

Let $(x_1,y_1)=(8,-2)$ and $(x_2,y_2)=(1,1)$. Then $m=\frac{1-(-2)}{1 - 8}=\frac{1 + 2}{1-8}=\frac{3}{-7}=-\frac{3}{7}$.
We can follow the same process for all pairs of points:

1. For $(4,3)$ and $(-1,6)$:

$m=\frac{6 - 3}{-1-4}=\frac{3}{-5}=-\frac{3}{5}$

1. For $(2,2)$ and $(-2,-2)$:

$m=\frac{-2 - 2}{-2-2}=\frac{-4}{-4}=1$

1. For $(6,-10)$ and $(6,14)$:

$m=\frac{14-(-10)}{6 - 6}=\frac{24}{0}$, slope is undefined since denominator is 0.

1. For $(5,-4)$ and $(9,-4)$:

$m=\frac{-4-(-4)}{9 - 5}=\frac{-4 + 4}{9-5}=\frac{0}{4}=0$

1. For $(11,7)$ and $(-6,2)$:

$m=\frac{2 - 7}{-6-11}=\frac{-5}{-17}=\frac{5}{17}$

1. For $(-3,5)$ and $(3,6)$:

$m=\frac{6 - 5}{3-(-3)}=\frac{1}{6}$

1. For $(-3,2)$ and $(7,2)$:

$m=\frac{2 - 2}{7-(-3)}=\frac{0}{10}=0$

1. For $(8,10)$ and $(-4,-6)$:

$m=\frac{-6 - 10}{-4-8}=\frac{-16}{-12}=\frac{4}{3}$

1. For $(-12,15)$ and $(18,-13)$:

$m=\frac{-13 - 15}{18-(-12)}=\frac{-28}{30}=-\frac{14}{15}$

1. For $(-8,6)$ and $(-8,4)$:

$m=\frac{4 - 6}{-8-(-8)}=\frac{-2}{0}$, slope is undefined.

1. For $(-8,-15)$ and $(-2,5)$:

$m=\frac{5-(-15)}{-2-(-8)}=\frac{5 + 15}{-2 + 8}=\frac{20}{6}=\frac{10}{3}$

1. For $(2,5)$ and $(3,6)$:

$m=\frac{6 - 5}{3-2}=1$

1. For $(6,1)$ and $(-6,1)$:

$m=\frac{1 - 1}{-6-6}=\frac{0}{-12}=0$

1. For $(4,6)$ and $(4,8)$:

$m=\frac{8 - 6}{4-4}=\frac{2}{0}$, slope is undefined.

1. For $(-5,-8)$ and $(-8,1)$:

$m=\frac{1-(-8)}{-8-(-5)}=\frac{1 + 8}{-8 + 5}=\frac{9}{-3}=-3$

1. For $(2,5)$ and $(-3,-5)$:

$m=\frac{-5 - 5}{-3-2}=\frac{-10}{-5}=2$

1. For $(9,8)$ and $(7,-8)$:

$m=\frac{-8 - 8}{7-9}=\frac{-16}{-2}=8$

1. For $(5,2)$ and $(5,-2)$:

$m=\frac{-2 - 2}{5-5}=\frac{-4}{0}$, slope is undefined.

1. For $(10,0)$ and $(-2,4)$:

$m=\frac{4 - 0}{-2-10}=\frac{4}{-12}=-\frac{1}{3}$

1. For $(17,18)$ and $(18,17)$:

$m=\frac{17 - 18}{18-17}=\frac{-1}{1}=-1$

1. For $(-6,-4)$ and $(4,1)$:

$m=\frac{1-(-4)}{4-(-6)}=\frac{1 + 4}{4 + 6}=\frac{5}{10}=\frac{1}{2}$

1. For $(-3,10)$ and $(-3,7)$:

$m=\frac{7 - 10}{-3-(-3)}=\frac{-3}{0}$, slope is undefined.

1. For $(2,-1)$ and $(-8,-2)$:

$m=\frac{-2-(-1)}{-8-2}=\frac{-2 + 1}{-10}=\frac{-1}{-10}=\frac{1}{10}$

1. For $(5,-9)$ and $(3,-2)$:

$m=\frac{-2-(-9)}{3-5}=\frac{-2 + 9}{3-5}=\frac{7}{-2}=-\frac{7}{2}$

1. For $(12,6)$ and $(3,-5)$:

$m=\frac{-5 - 6}{3-12}=\frac{-11}{-9}=\frac{11}{9}$

1. For $(-4,5)$ and $(-8,-5)$:

$m=\frac{-5 - 5}{-8-(-4)}=\frac{-10}{-4}=\frac{5}{2}$

Answer:

1. $-\frac{3}{5}$
2. $-\frac{3}{7}$
3. $1$
4. Undefined
5. $0$
6. $\frac{5}{17}$
7. $\frac{1}{6}$
8. $0$
9. $\frac{4}{3}$
10. $-\frac{14}{15}$
11. Undefined
12. $\frac{10}{3}$
13. $1$
14. $0$
15. Undefined
16. $-3$
17. $2$
18. $8$
19. Undefined
20. $-\frac{1}{3}$
21. $-1$
22. $\frac{1}{2}$
23. Undefined
24. $\frac{1}{10}$
25. $-\frac{7}{2}$
26. $\frac{11}{9}$
27. $\frac{5}{2}$