1. **State the problem:** We are given two points $A(-6,5)$ and $B(-2,-3)$ and need to find the equation of the line of reflection between them. 2. **Understanding the line of reflection:** The line of reflection is the perpendicular bisector of the segment joining the two points. It passes through the midpoint of $AB$ and is perpendicular to the line segment $AB$. 3. **Find the midpoint $M$ of $AB$:** $$M = \left(\frac{-6 + (-2)}{2}, \frac{5 + (-3)}{2}\right) = \left(\frac{-8}{2}, \frac{2}{2}\right) = (-4, 1)$$ 4. **Find the slope of line segment $AB$:** $$m_{AB} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 5}{-2 - (-6)} = \frac{-8}{4} = -2$$ 5. **Find the slope of the perpendicular bisector:** The slope of the perpendicular bisector $m_{perp}$ is the negative reciprocal of $m_{AB}$: $$m_{perp} = -\frac{1}{m_{AB}} = -\frac{1}{-2} = \frac{1}{2}$$ 6. **Write the equation of the line of reflection:** Using point-slope form with point $M(-4,1)$ and slope $\frac{1}{2}$: $$y - 1 = \frac{1}{2}(x - (-4))$$ $$y - 1 = \frac{1}{2}(x + 4)$$ 7. **Simplify the equation:** $$y - 1 = \frac{1}{2}x + 2$$ $$y = \frac{1}{2}x + 3$$ **Final answer:** The equation of the line of reflection is $$y = \frac{1}{2}x + 3$$.