To find the slope of the line that contains the points $(-2, -2)$ and $(4, 2)$, we can use the slope formula:

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

Where:

• $(x_1, y_1) = (-2, -2)$
• $(x_2, y_2) = (4, 2)$

Now, substituting the values into the formula:

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

So, the slope of the line is:

$\boxed{\frac{2}{3}}$

Thus, the correct answer is C.

Would you like a detailed explanation or have any further questions? Here are some related questions for further practice:

1. What is the slope if the points were $(2, 3)$ and $(5, 7)$?
2. How would the slope change if the y-coordinates of both points were negative?
3. Can you derive the equation of the line in slope-intercept form?
4. What is the importance of the slope in analyzing linear equations?
5. How does the graph of a line with slope $-\frac{2}{3}$ look compared to $\frac{2}{3}$?

Tip: When finding the slope, remember that it measures how much the y-value changes for each unit change in the x-value.