find the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
We require to find the slope and the midpoint of the given line segment
Find the slope using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (1, - 2 )
m = [tex]\frac{-2-4}{1+3}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
the slope of the perpendicular is the negative inverse of m
[tex]m_{perpendicular}[/tex] = [tex]\frac{2}{3}[/tex]
Find the midpoint using the midpoint formula
midpoint = [ [tex]\frac{1}{2}[/tex](- 3 + 1), [tex]\frac{1}{2}[/tex](4 - 2)] = (- 1, 1)
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 1, 1 ) into the partial equation
1 = - [tex]\frac{2}{3}[/tex] + c ⇒ c = [tex]\frac{8}{3}[/tex]
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of perpendicular bisector
