Write the equation of the perpendicular bisector of the line segment AB with endpoints A(1,1) and B(7,5). Write your answer in slope intercept form.

not math its like algebra or calculus or something please change subject name

To find the equation of the perpendicular bisector of the line segment AB with endpoints A(1,1) and B(7,5), follow these steps:

1. Find the midpoint of the line segment AB:
- The midpoint (M) is the average of the x-coordinates and the average of the y-coordinates of A and B.
- x-coordinate of the midpoint (Mx) = (1 + 7) / 2 = 8 / 2 = 4
- y-coordinate of the midpoint (My) = (1 + 5) / 2 = 6 / 2 = 3
- So, the midpoint (M) is (4, 3).

2. Find the slope of the line segment AB:
- The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).
- x1 = 1, y1 = 1, x2 = 7, y2 = 5
- m = (5 - 1) / (7 - 1) = 4 / 6 = 2 / 3

3. Find the negative reciprocal of the slope of AB:
- The negative reciprocal of a slope is obtained by flipping the fraction and changing its sign.
- The negative reciprocal of 2 / 3 is -3 / 2.

4. Write the equation of the perpendicular bisector in slope-intercept form (y = mx + b):
- Using the midpoint (4, 3) and the negative reciprocal of the slope (-3 / 2), we can substitute them into y = mx + b.
- 3 = (-3 / 2) * 4 + b (using the midpoint and the negative reciprocal slope)
- 3 = -6 + b
- b = 9

5. Substitute the slope and the y-intercept into the equation:
- The equation of the perpendicular bisector is: y = (-3 / 2)x + 9

Therefore, the equation of the perpendicular bisector of the line segment AB with endpoints A(1,1) and B(7,5) in slope-intercept form is: y = (-3 / 2)x + 9.