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To find the equation of the line that reflects point \( B \) at \( (2, -4) \) to point \( B' \) at \( (6, -4) \), let's go through the steps.

### Step-by-Step Solution:

1. **Determine the Midpoint of \( B \) and \( B' \)**: 
   Since the line of reflection will be the perpendicular bisector of the segment joining \( B \) and \( B' \), let's first find the midpoint \( M \) of \( B \) and \( B' \).

   \[
   M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
   \]
   where \( B = (2, -4) \) and \( B' = (6, -4) \).

   \[
   M = \left( \frac{2 + 6}{2}, \frac{-4 + (-4)}{2} \right) = (4, -4)
   \]

2. **Determine the Slope of \( BB' \)**:
   The slope of the line segment \( BB' \) can be found as follows:

   \[
   \text{slope of } BB' = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-4)}{6 - 2} = \frac{0}{4} = 0
   \]

   Since the slope is 0, \( BB' \) is a horizontal line.

3. **Find the Perpendicular Line (Line of Reflection)**:
   The line of reflection will be perpendicular to \( BB' \). Since \( BB' \) is horizontal, the line of reflection must be vertical.

   The vertical line passing through the midpoint \( M = (4, -4) \) has the equation:

   \[
   x = 4
   \]

### Conclusion:
The equation of the line of reflection is:
\[
x = 4
\]

Would you like more details or have questions?

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### Related Questions:
1. How do you find the equation of a line when given two points?
2. What is the relationship between perpendicular slopes in geometry?
3. How can you verify that a point is reflected correctly across a line?
4. How does the midpoint formula work in coordinate geometry?
5. What is the significance of horizontal and vertical lines in reflections?

### Tip:
For reflections across a line, always consider finding the midpoint and ensuring the line is the perpendicular bisector of the line segment connecting the original and reflected points.

Point B' is the image of point B after a reflection in a line. Write an equation of the line.

B(2, -4), B'(6, -4)

Learn how to find the equation of the reflection line for points B(2, -4) and B'(6, -4) in this geometry problem. The solution includes the use of midpoint and slope formulas to determine the line of reflection.

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