To find the slope of the line that passes through the points $(6, 4)$ and $(9, 3)$, you can use the slope formula:

$\text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}$

Here, $(x_1, y_1) = (6, 4)$ and $(x_2, y_2) = (9, 3)$. Substituting these values into the formula:

$m = \frac{3 - 4}{9 - 6} = \frac{-1}{3}$

So, the slope of the line is $\boxed{-\frac{1}{3}}$.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

1. What is the equation of the line passing through the same points?
2. How do you find the y-intercept given the slope and one point?
3. How do you determine if two lines are parallel?
4. What is the slope of a line perpendicular to the line you just calculated?
5. How does the slope of a line affect its steepness?

Tip: The slope of a line indicates how much the y-value changes for each unit increase in the x-value. A negative slope means the line is decreasing, while a positive slope means it's increasing.