Find the equation of line passing through point (2,-5) which is
(i) parallel to the line 3x + 2y - 4 = 0
(ii) perpendicular to the line 3x + 2y - 4 =0

Explanation

(i) Equation of line parallel to the line 3x + 2y - 4 = 0 is
3x + 2y + `lambda` = 0
If this line passes through (2, - 5), then
3(2) + 2(-5) + `lambda` = 0
`therefore lambda = 4`
So, equation of line is 3x + 2y + 4 =0
Alternative method:
Slope of given line 3x + 2y - 4 = 0 is `-(3)/(2)`.
Thus, equation of line through point (2,-5) having slope `-(3)/(2)` is
`y + 5 = -(3)/(2)(x-2)`
or 3x + 2y + 4 = 0
(ii) Equation of line perpendicular to the line 3x + 2y - 4 = 0 is
`2x - 3y + lambda = 0`

If this line passes through (2,-5), then
`2(2)-3(-5) + lambda = 0`
`therefore lambda = -19`
So, equation of line is 2x - 3y - 19 = 0.
Alternative method:
Slope of line perpendicular to the line ` 3x + 2y - 4 = 0 "is" (2)/(3)`.
Thus, equation of line through point (2,-5) having slope `(2)/(3)` is
` y + 5 = (2)/(5) (x-2)`
or 2x-3y-19 = 0