From the uploaded image, we are tasked to identify the slope of the line of reflection that maps the pink triangle to the blue triangle.

To solve this:

1. Find the line of reflection: The line of reflection will be the perpendicular bisector of the segment connecting corresponding points from the pink and blue triangles.

2. Determine the slope of the line:

   • Observe the dotted lines connecting corresponding points between the pink and blue triangles.
   • Each dotted line crosses the line of reflection at a right angle (90 degrees), implying their slopes are negative reciprocals of the slope of the reflection line.

Observations from the Image

• One dotted line connects a point at $(4, 5)$ in the pink triangle to $(4, -5)$ in the blue triangle.
• The midpoint of this dotted line lies on the line of reflection: Midpoint = $(4, 0)$.
• The reflection line must pass through this midpoint and have a slope such that it is perpendicular to the dotted line.

Calculation of Slopes

• Slope of one dotted line: Since the points are vertically aligned, the slope of this dotted line is undefined (vertical line).

• The line of reflection is horizontal because it is perpendicular to a vertical line. Thus, its slope is $0$.

Final Answer

• Slope of one of the dotted lines: Undefined (vertical line).
• Slope of the line of reflection: $0$ (horizontal line).

Would you like me to verify any details or explain further?

Here are related questions to expand on:

1. What is the equation of the line of reflection in this example?
2. How do we derive the midpoint of a segment geometrically?
3. What are the properties of reflections over horizontal or vertical lines?
4. Can reflection lines have slopes other than $0$ or undefined? If so, when?
5. How do the slopes of perpendicular lines relate in general?

Tip: Always identify the perpendicular bisector as the line of reflection to simplify mapping between figures.