Question

1. endpoint: (-3, 2), midpoint: (9, 0)

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

1. (2, 1), (15, 10)
2. (-5, -16), (-14, -5)
3. (11, 18), (13, -17)
4. (-10, -1), (-17, 14)
5. (-12, 9), (7, 0)

Explanation:

Step1: Recall slope - formula

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

Step2: Solve for problem 21

For points $(2,1)$ and $(15,10)$, let $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(15,10)$. Then $m=\frac{10 - 1}{15 - 2}=\frac{9}{13}$.

Step3: Solve for problem 22

For points $(-5,-16)$ and $(-14,-5)$, let $(x_1,y_1)=(-5,-16)$ and $(x_2,y_2)=(-14,-5)$. Then $m=\frac{-5-(-16)}{-14 - (-5)}=\frac{-5 + 16}{-14 + 5}=\frac{11}{-9}=-\frac{11}{9}$.

Step4: Solve for problem 23

For points $(11,18)$ and $(13,-17)$, let $(x_1,y_1)=(11,18)$ and $(x_2,y_2)=(13,-17)$. Then $m=\frac{-17 - 18}{13 - 11}=\frac{-35}{2}=-\frac{35}{2}$.

Step5: Solve for problem 24

For points $(-10,-1)$ and $(-17,14)$, let $(x_1,y_1)=(-10,-1)$ and $(x_2,y_2)=(-17,14)$. Then $m=\frac{14-(-1)}{-17-(-10)}=\frac{14 + 1}{-17 + 10}=\frac{15}{-7}=-\frac{15}{7}$.

Step6: Solve for problem 25

For points $(-12,9)$ and $(7,0)$, let $(x_1,y_1)=(-12,9)$ and $(x_2,y_2)=(7,0)$. Then $m=\frac{0 - 9}{7-(-12)}=\frac{-9}{7 + 12}=-\frac{9}{19}$.

Answer:

1. $\frac{9}{13}$
2. $-\frac{11}{9}$
3. $-\frac{35}{2}$
4. $-\frac{15}{7}$
5. $-\frac{9}{19}$