find the slope of the line through each pair of points.\n9) (8, 10), (-7, 14)\n10) (-3, 1), (-17, 2)\n11)…

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 problem 9

For points $(8,10)$ and $(-7,14)$, $x_1 = 8,y_1=10,x_2=-7,y_2 = 14$. Then $m=\frac{14 - 10}{-7 - 8}=\frac{4}{-15}=-\frac{4}{15}$.

Step3: Solve for problem 10

For points $(-3,1)$ and $(-17,2)$, $x_1=-3,y_1 = 1,x_2=-17,y_2=2$. Then $m=\frac{2 - 1}{-17+3}=\frac{1}{-14}=-\frac{1}{14}$.

Step4: Solve for problem 11

For points $(-20,-4)$ and $(-12,-10)$, $x_1=-20,y_1=-4,x_2=-12,y_2=-10$. Then $m=\frac{-10 + 4}{-12+20}=\frac{-6}{8}=-\frac{3}{4}$.

Step5: Solve for problem 12

For points $(-12,-5)$ and $(0,-8)$, $x_1=-12,y_1=-5,x_2 = 0,y_2=-8$. Then $m=\frac{-8 + 5}{0 + 12}=\frac{-3}{12}=-\frac{1}{4}$.

Step6: Solve for problem 13

For points $(-19,-6)$ and $(15,16)$, $x_1=-19,y_1=-6,x_2=15,y_2=16$. Then $m=\frac{16 + 6}{15+19}=\frac{22}{34}=\frac{11}{17}$.

Step7: Solve for problem 14

For points $(-6,9)$ and $(7,-9)$, $x_1=-6,y_1=9,x_2=7,y_2=-9$. Then $m=\frac{-9 - 9}{7+6}=\frac{-18}{13}=-\frac{18}{13}$.

Step8: Solve for problem 15

For points $(-18,-20)$ and $(-18,-15)$, $x_1=-18,y_1=-20,x_2=-18,y_2=-15$. Since $x_2 - x_1=-18+18 = 0$, the slope is undefined.

Step9: Solve for problem 16

For points $(12,-18)$ and $(11,12)$, $x_1=12,y_1=-18,x_2=11,y_2=12$. Then $m=\frac{12 + 18}{11 - 12}=\frac{30}{-1}=-30$.

Answer:

9. $-\frac{4}{15}$
10. $-\frac{1}{14}$
11. $-\frac{3}{4}$
12. $-\frac{1}{4}$
13. $\frac{11}{17}$
14. $-\frac{18}{13}$
15. Undefined
16. $-30$