When you look at a linear equation and reflect it, the slope behaves in some interesting ways, depending on which axis you are flipping it over. Let’s break it down!

1. Reflection Over the x-axis:

   • When you reflect a graph over the x-axis, the y-coordinates of each point will change signs.
   • For a line with the equation (y = mx + b), it changes to (y = -mx + b).
   • Effect on Slope: The slope will also change to the opposite sign.
     For example, if the original slope was (2), after reflection, it becomes (-2).

2. Reflection Over the y-axis:

   • Here, the x-coordinates change signs.
   • The equation (y = mx + b) also changes to (y = -mx + b).
   • Effect on Slope: Just like with the x-axis, the slope changes to the opposite sign.
     So again, a slope of (2) becomes (-2).

3. General Summary:

   • Reflecting a line over either axis makes the slope change signs, but the y-intercept stays the same.

Understanding these reflections helps you see how lines change in different situations. This is really important for getting better at algebra!