Question

find the slope of the line containing each pair of points.

1. a(3, 9), b(1, 5)
2. a(7, 5), b(2, 4)
3. a(-3, 10), b(-5, -4)
4. a(5, 2), b(2, -1)
5. a(3, -2), b(-1, 3)
6. a(-1, 3), b(5, 3)
7. a(1, 8), b(-1, 7)
8. a(2, 6), b(3, -4)
9. a(0, 4), b(3, -2)
10. a(6, -1), b(5, 6)
11. a(-9, 9), b(7, -2)
12. a(3, 7), b(-1, -1)

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 problem 17

Let $A(3,9)$ be $(x_1,y_1)$ and $B(1,5)$ be $(x_2,y_2)$. Then $m=\frac{5 - 9}{1 - 3}=\frac{-4}{-2}=2$.

Step3: For problem 18

Let $A(7,5)$ be $(x_1,y_1)$ and $B(2,4)$ be $(x_2,y_2)$. Then $m=\frac{4 - 5}{2 - 7}=\frac{-1}{-5}=\frac{1}{5}$.

Step4: For problem 19

Let $A(-3,10)$ be $(x_1,y_1)$ and $B(-5,-4)$ be $(x_2,y_2)$. Then $m=\frac{-4 - 10}{-5+3}=\frac{-14}{-2}=7$.

Step5: For problem 20

Let $A(5,2)$ be $(x_1,y_1)$ and $B(2,-1)$ be $(x_2,y_2)$. Then $m=\frac{-1 - 2}{2 - 5}=\frac{-3}{-3}=1$.

Step6: For problem 21

Let $A(3,-2)$ be $(x_1,y_1)$ and $B(-1,3)$ be $(x_2,y_2)$. Then $m=\frac{3 + 2}{-1 - 3}=\frac{5}{-4}=-\frac{5}{4}$.

Step7: For problem 22

Let $A(-1,3)$ be $(x_1,y_1)$ and $B(5,3)$ be $(x_2,y_2)$. Then $m=\frac{3 - 3}{5 + 1}=0$.

Step8: For problem 23

Let $A(1,8)$ be $(x_1,y_1)$ and $B(-1,7)$ be $(x_2,y_2)$. Then $m=\frac{7 - 8}{-1 - 1}=\frac{-1}{-2}=\frac{1}{2}$.

Step9: For problem 24

Let $A(2,6)$ be $(x_1,y_1)$ and $B(3,-4)$ be $(x_2,y_2)$. Then $m=\frac{-4 - 6}{3 - 2}=-10$.

Step10: For problem 25

Let $A(0,4)$ be $(x_1,y_1)$ and $B(3,-2)$ be $(x_2,y_2)$. Then $m=\frac{-2 - 4}{3 - 0}=\frac{-6}{3}=-2$.

Step11: For problem 26

Let $A(6,-1)$ be $(x_1,y_1)$ and $B(5,6)$ be $(x_2,y_2)$. Then $m=\frac{6 + 1}{5 - 6}=\frac{7}{-1}=-7$.

Step12: For problem 27

Let $A(-9,9)$ be $(x_1,y_1)$ and $B(7,-2)$ be $(x_2,y_2)$. Then $m=\frac{-2 - 9}{7 + 9}=\frac{-11}{16}$.

Step13: For problem 28

Let $A(3,7)$ be $(x_1,y_1)$ and $B(-1,-1)$ be $(x_2,y_2)$. Then $m=\frac{-1 - 7}{-1 - 3}=\frac{-8}{-4}=2$.

Answer:

1. $2$
2. $\frac{1}{5}$
3. $7$
4. $1$
5. $-\frac{5}{4}$
6. $0$
7. $\frac{1}{2}$
8. $-10$
9. $-2$
10. $-7$
11. $-\frac{11}{16}$
12. $2$