Question

1. rise: - 3; run: 4

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

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: Take an example (for problem 17)

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

Step3: Generalize for other problems

For any two - point pair $(x_1,y_1)$ and $(x_2,y_2)$ in the given problems, substitute into the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ to find the slope.

Since we don't have a specific pair of points chosen to solve for a single answer, the general process to find the slope of a line passing through two given points is as above. If you want to solve for a particular problem number (e.g., 17, 19, etc.), you can substitute the coordinates of the two points into the slope formula. For example, for problem 19 with $A(-3,10)$ and $B(-5,-4)$:
Let $(x_1,y_1)=(-3,10)$ and $(x_2,y_2)=(-5,-4)$. Then $m=\frac{-4 - 10}{-5+3}=\frac{-14}{-2}=7$.

If we assume we are solving problem 17:

Answer:

2