To determine the slope of a line perpendicular to the given line segment $\overline{AB}$, we need to:

1. Calculate the slope of $\overline{AB}$:

   • The coordinates for points $A$ and $B$ appear to be approximately:
     • $A(-3, -3)$
     • $B(1, 2)$
   • Using the slope formula: $\text{slope of } AB = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-3)}{1 - (-3)} = \frac{2 + 3}{1 + 3} = \frac{5}{4}$

2. Find the slope of the perpendicular line:

   • The slope of a line perpendicular to another is the negative reciprocal. So, the perpendicular slope is: $-\frac{4}{5}$

3. Identify the correct answer:

   • The slope that is perpendicular to $\overline{AB}$ is $-\frac{4}{5}$, but since this specific option isn't listed, let's verify if the question might imply a different value or a calculation is missed.

Let me know if this needs further clarification or if there are questions about other possible interpretations of the options. Here are five follow-up questions for exploration:

1. How do we determine the midpoint of $\overline{AB}$ given points $A$ and $B$?
2. Why do perpendicular slopes involve a negative reciprocal relationship?
3. What would be the equation of a line passing through point $A$ and perpendicular to $\overline{AB}$?
4. How can we verify if two lines are perpendicular solely by looking at their slopes?
5. What is the process of finding the distance between points $A$ and $B$?

Tip: Remember that the negative reciprocal of a slope is the key to identifying perpendicular lines on a coordinate plane.