Question

Write the equation of the line perpendicular to y = 6/5x + 4/5 that passes through the point (-3,2).

Answer 1

Answer:

The equation of the perpendicular line of the given line is

 $y = \frac{-5}{6} x -\frac{1}{2}$

Step-by-step explanation:

Step(i):-

Given the equation of the line

         $y = \frac{6}{5} x + \frac{4}{5}$

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

                                          $y = \frac{-5}{6} x -\frac{3}{6}$

Final answer:-

The equation of the perpendicular line of the given line is

 $y = \frac{-5}{6} x -\frac{1}{2}$