Find The Equation Of The Perpendicular Bisector Of The Line Joining The Points A(4,2) And B(-6,4)?

The slope of the given segment is 2/-10 = -1/5, so the slope of the required bisector is 5.
The midpoint of the given segment is (-1, 3), so the line will have an equation
y - 3 = 5(x + 1)
In slope-intercept form, that is

y = 5x + 8