To solve the problem of finding the slope of the line passing through the points $(8, 9)$ and $(1, 1)$, we use the slope formula:

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

Step 1: Assign the coordinates

Let: $(x_1, y_1) = (8, 9) \quad \text{and} \quad (x_2, y_2) = (1, 1).$

Step 2: Plug the values into the formula

$m = \frac{1 - 9}{1 - 8}$

Step 3: Simplify

$m = \frac{-8}{-7}$

$m = \frac{8}{7} \quad \text{(simplified to an improper fraction)}.$

Final Answer:

The slope of the line is: $\boxed{\frac{8}{7}}$

Would you like a deeper explanation or have more questions about this?

Here are 5 related questions to expand on this topic:

1. How would you write the equation of the line passing through these two points in slope-intercept form?
2. Can you explain what the slope tells us about the direction of the line?
3. How do we interpret negative slopes compared to positive slopes?
4. What are some real-world examples of interpreting slope in different contexts?
5. How do you calculate the slope if only one point and the slope-intercept equation are given?

Tip: Always simplify fractions completely and double-check for sign errors when calculating slope!