Final answer:
The equation for the perpendicular bisector of the segment with endpoints E(-5, -3) and F(-3,7) in point-slope form is y = (-1/5)x + (6/5).
Step-by-step explanation:
To find the equation of the perpendicular bisector of a line segment, we need to find its midpoint and its perpendicular slope. The midpoint of the segment with endpoints E(-5, -3) and F(-3, 7) is ((-5-3)/2, (-3+7)/2) = (-4, 2). The slope of the original segment is (7-(-3))/(-3-(-5)) = 10/2 = 5. Since the perpendicular slope is the negative reciprocal of the original slope, the perpendicular slope is -1/5.
Now, we can use the point-slope form of a line to write the equation. The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we have y - 2 = (-1/5)(x - (-4)). Simplifying, we get y - 2 = (-1/5)x - (4/5), which can be rearranged as y = (-1/5)x + (6/5).