Answer:
4. The equation of the perpendicular bisector is y = 
 x - 
 
5. The equation of the perpendicular bisector is y = - 2x + 16
6. The equation of the perpendicular bisector is y = 
 x + 
 
Step-by-step explanation:
Lets revise some important rules
- The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is 
 (reciprocal m and change its sign) - The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
 - The formula of the slope of a line is 
  - The mid point of a segment whose end points are 
 and 
 is 
  - The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept 
 
4.
∵ The line passes through (7 , 2) and (4 , 6)
- Use the formula of the slope to find its slope
∵ 
 = 7 and 
 = 4
∵ 
 = 2 and 
 = 6
∴ 
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line = 
 
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point = 
∴ The mid-point = 
- Substitute the value of the slope in the form of the equation
∵ y = 
 x + b
- To find b substitute x and y in the equation by the coordinates 
    of the mid-point
∵ 4 = 
 × 
 + b
∴ 4 = 
 + b
- Subtract  
 from both sides
∴ 
 = b
∴ y = 
 x - 
 
∴ The equation of the perpendicular bisector is y = 
 x - 
 
5.
∵ The line passes through (8 , 5) and (4 , 3)
- Use the formula of the slope to find its slope
∵ 
 = 8 and 
 = 4
∵ 
 = 5 and 
 = 3
∴ 
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line = -2
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point = 
∴ The mid-point = 
∴ The mid-point = (6 , 4)
- Substitute the value of the slope in the form of the equation
∵ y = - 2x + b
- To find b substitute x and y in the equation by the coordinates 
    of the mid-point
∵ 4 = -2 × 6 + b
∴ 4 = -12 + b
- Add 12 to both sides
∴ 16 = b
∴ y = - 2x + 16
∴ The equation of the perpendicular bisector is y = - 2x + 16
6.
∵ The line passes through (6 , 1) and (0 , -3)
- Use the formula of the slope to find its slope
∵ 
 = 6 and 
 = 0
∵ 
 = 1 and 
 = -3
∴ 
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line = 
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point = 
∴ The mid-point = 
∴ The mid-point = (3 , -1)
- Substitute the value of the slope in the form of the equation
∵ y = 
 x + b
- To find b substitute x and y in the equation by the coordinates 
    of the mid-point
∵ -1 = 
 × 3 + b
∴ -1 = 
 + b 
- Add  
  to both sides
∴ 
 = b
∴ y = 
 x + 
 
∴ The equation of the perpendicular bisector is y = 
 x +