Respuesta :
Answer:
The equation of the perpendicular line of the given line is
[tex]y = \frac{-5}{6} x -\frac{1}{2}[/tex]
Step-by-step explanation:
Step(i):-
Given the equation of the line
[tex]y = \frac{6}{5} x + \frac{4}{5}[/tex]
cross-multiplication, we get
5y = 6x +4
The equation of the straight line is 6x - 5y +4=0
The equation of the perpendicular line to the given line is
b x - ay +k=0
The equation of the perpendicular line to the given line is -5x-6y +k=0
This line passes through the point (-3,2)
⇒ - 5(-3) -6(2)+k=0
⇒ 15 -12 +k=0
⇒ 3 +k=0
⇒ k =-3
Step(ii):-
The equation of the perpendicular line is
-5x-6y-3=0
5x + 6y +3 =0
6y = -5x-3
[tex]y = \frac{-5}{6} x -\frac{3}{6}[/tex]
Final answer:-
The equation of the perpendicular line of the given line is
[tex]y = \frac{-5}{6} x -\frac{1}{2}[/tex]
