Find the equation in slopeintercept form of the line that is

Find the equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3, 2) and (3, -8). Show all calculations.

Solution

Given

the line segemnt passes through (-3,2) and (3,-8)

slope of this line segment (m) = ( y₂ - y₁ ) / (x₂ - x₁)

                            m = ( -8 - (2)) / (3 - (-3))

                         m = ( -8 -2 ) / (3 + 3)

                        m = (-10)/ 6

                       m = -5/3

slope of the perpendicular bisector =

product of slopes of two perpendicular lines = -1

m * (slope of perpendicular bisector) = -1

(-5 / 3) * (slope of perpendicular bisector) = -1

slope of perpendicular bisector = 3/5

the perpendicular bisector bisects the line and will pass through the midpoint of the given points

midpoint of (-3, 2) and (3,-8)

midpoint = (x₁ + x₂ ) / 2 , (y₁ + y₂) / 2

               = 0 , -3

now the equation of perpendicular bisector

y - y₁ = m (x - x₁)

y - (-3) = (3/5 ) * (x - 0)

y + 3 = 3x / 5                                   //       - (-3) = 3

5y + 15 = 3x

slope intercept form = y = mx + b

now

5y = 3x - 15

y = 3x/5 - 15/5

y = 3x/5 - 3