Question

what is the equation for a line perpendicular to the line 3x+2y=6 passing through (1,-2)

Answer 1

A perpedicular line to L has a gradient equal to the negative reciprocal of that of L.
L:3x+2y-6=0 => N:2x-3y+c=0
Plugging in (1,-2) as a point on N we get 2+6+c=0 +>c=-8
N:2x-3y=8

Answer 2

Write 3x + 2y = 6 in standard form........... y = mx + c
2y = -3x + 6 then devide both sides by 2
y= -3/2x + 3.........................(i) mi = -3/2
but m of perpendicular line is - reciprocal of mi, thus 2/3
so y = 2/3x + c
to get c we substitute values of 1,-2) in the equation
-2 = 2/3(1) + c
c = -2 - 2/3............... =-5/3
substituting -5/3 with,we have y = 2/3x +(-5/3)
y = 2/3x - 5/3 as the equation of perpendicular line.