To find the slope of the line passing through the points $(-4, 8)$ and $(6, 9)$, we can use the slope formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

• $(x_1, y_1)$ is the first point $(-4, 8)$,
• $(x_2, y_2)$ is the second point $(6, 9)$.

Substitute the coordinates into the formula:

$\text{slope} = \frac{9 - 8}{6 - (-4)} = \frac{1}{6 + 4} = \frac{1}{10}$

Thus, the slope is $\frac{1}{10}$, which is a positive slope.

Now let's check the verticality or horizontality:

• Since the x-coordinates are different ($-4$ and $6$), the line is not vertical.
• Since the slope is not 0, the line is not horizontal.

So, the line rises (since the slope is positive).

Answer:

• The slope is $\frac{1}{10}$.
• The line rises.

Would you like further clarification on this problem, or do you have additional questions? Here are some related questions you might find helpful:

1. How do you calculate the slope when the points have the same y-coordinate?
2. What does it mean for a line to be vertical, and how can we determine its slope?
3. How do we interpret a slope of 0?
4. What is the difference between a positive and negative slope?
5. Can you solve for the equation of a line given two points?

Tip: When calculating slope, always ensure that the denominator (the difference in x-coordinates) is not zero, as division by zero is undefined.