To determine the slope of the line passing through the points $(2, 2)$ and $(5, 6)$, we use the slope formula:

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

Here,
$(x_1, y_1) = (2, 2)$ and $(x_2, y_2) = (5, 6)$.

Substitution:

$m = \frac{6 - 2}{5 - 2}$

Simplify:

$m = \frac{4}{3}$

Final Answer:

The slope of the line is $\frac{4}{3}$ (an improper fraction).

Would you like a further explanation on slopes or graphing lines? Let me know!

Related Questions:

1. How do you find the slope when given two points?
2. What does the slope $\frac{4}{3}$ mean in a real-world context?
3. Can you write the equation of the line with slope $\frac{4}{3}$ and passing through $(2, 2)$?
4. How do you determine if two lines are parallel or perpendicular?
5. What is the slope of a vertical or horizontal line?

Tip: When solving for the slope, always subtract the $y$-values and $x$-values in the same order!