The equation in slope-intercept form, of the perpendicular bisector of the given line segment, is [tex]\rm y = -4x - 6[/tex].
Given
The given line segment has a midpoint at (−1, −2).
Let AB be segmented with midpoint M(-1,-2).
The perpendicular bisector line always passes through the midpoint of the segment.
So, the equation satisfies the given midpoints.
Put x =-1 and y =-2 into the equation and we get;
Then,
[tex]\rm y = -4x -6\\\\y+4x=-6\\\\-2+4(-1)=-6\\\\-2-4=-6\\\\-6=-6[/tex]
Hence, the equation in slope-intercept form, of the perpendicular bisector of the given line segment is [tex]\rm y = -4x - 6[/tex].
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