Question

Find the value of m if the lines represented by 2mx-3y=1 and y=1-2x are perpendicular to each other

Answer 1

so slope for line 2mx - 3y = 1 is m = 2m/3
and slope for line 2x + y = 1 is m₁ = -2

so two lines are perpendicular when

m x m₁ = -1

so ⇒2m/3 x -2 = -1
   ⇒4m/3= 1
m = 3/4 ANSWER

Answer 2

     2 m x - 3 y = 1,     y = 2m/3 x  - 1/3     => slope = 2m/3 

    y = 1 - 2x      =>   slope = -2  

when two lines are perpendicular, product of their slopes = -1

      -2 * 2m /3 = -1     =>  m = 3/4