Let's solve the slope for each of the lines passing through the given points as depicted in the uploaded image.

Formula to Find the Slope:

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Problem 8:

Given points: $(-1, -4)$ and $(2, 2)$

Using the slope formula:

$m = \frac{2 - (-4)}{2 - (-1)} = \frac{2 + 4}{2 + 1} = \frac{6}{3} = 2$

The slope for problem 8 is $m = 2$.

Problem 9:

Given points: $(-3, 4)$ and $(3, -1)$

Using the slope formula:

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

The slope for problem 9 is $m = -\frac{5}{6}$.

Would you like to go over any of the remaining problems (10–15), or would you like more details on these two?

Relative Questions:

1. What is the geometric meaning of the slope?
2. How does the slope relate to the angle a line makes with the x-axis?
3. What is the slope of a vertical line, and why?
4. What happens to the slope if two points on the line are very close to each other?
5. How can we find the equation of the line given the slope and one point?

Tip:

Remember, if two points have the same x-coordinate, the slope is undefined since division by zero is not possible. This corresponds to a vertical line.