Question

Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.

Answer 1

3x - 2y = 5
2y = 3x - 5
y = (3/2) x - 5/2

so the gradient (m)  of the required line = -1 / (3/2) = -2/3

using the general form 

  y - y1 = m(x - x1)  ,                m = -2/3 , x1 = -2 and y1 = 1

 y - 1 = -(2/3) ( x - (-2))


y = -(2/3)x - 4/3 + 1

y = -(2/3)x  - 1/3 

multiply through by 3

3y = - 2x  - 1 

in standard form its

2x + 3y = -1