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Answer:
2x +y = -2
Explanation:
The bisector must have a slope that is the negative reciprocal of the slope of the line between these points. It must pass through the midpoint of the segment.
The slope of the line through the given points is ...
m = (y2 -y1)/(x2 -x1)
= (5 -(-1))/(4 -(-8)) = 6/12 = 1/2
The slope of the required bisector is then ...
m = -1/(1/2) = -2
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The midpoint of the given segment is ...
((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)
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Then the point-slope form of the equation of the bisector is ...
y -y1 = m(x -x1)
y -2 = -2(x -(-2))
y = -2x -4 +2
y = -2x -2 . . . . . . . slope-intercept form equation
2x +y = -2 . . . . . . . standard form equation