https://file.aiquickdraw.com/mathbot/file/1728842875119js8pa49i.jpg

In the image, it asks for the equation of the line of reflection, and we are given that the slope of the reflection line is \( -1 \).

The general form of the equation of a line is:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.

Given that the slope \( m \) is \( -1 \), the equation so far is:
\[
y = -x + b
\]

To find \( b \), the y-intercept, we need a point that lies on the line of reflection. Based on the image, it looks like the line of reflection is passing through the origin (0, 0). If this is the case, we substitute \( (0, 0) \) into the equation:

\[
0 = -(0) + b
\]

This gives \( b = 0 \), so the equation of the line of reflection is:
\[
y = -x
\]

Would you like further explanation on the process? 

Here are five related questions to explore:
1. How can you determine the equation of a line if you know its slope and a point on the line?
2. What is the geometric significance of a line of reflection?
3. How does the slope of the line of reflection affect the shape of the reflected figure?
4. Can a line of reflection have any other slope, or is it always related to the slopes of the shapes being reflected?
5. How do you find the equation of a line parallel or perpendicular to a given line?

**Tip:** The slope of perpendicular lines is the negative reciprocal of each other.

Learn how to find the equation of a line of reflection given the slope of the line. This problem involves using the slope-intercept form and understanding the geometric significance of reflection. Suitable for students in Grades 8-10.

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