algebra question?

Question

whoever can explain this AND GETS AN ANSWER THAT IS RIGHT I WILL GIVE YOU 10 POINTS
write in standard form
perpendicular to (1,1)(-3,2) thru (4,-2)

Answer 1

Slope of line =(y2 -y1)/ (x2 -x1)=(2-1)/(-3 -1)=- (1/4)
Therefore slope of a line perpendicular is 4
To find the equation having slope 4 and passing through (4,-2)
y = mx +a
y =4x +a
-2 =4(4) +a
a = -18
Therefore the equation is
y =4x -18 or 4x -y -18 =0

Answer 2

1) All lines that pass through the point (4,-2) is given by:
y +2 = m(x-4) where m is the angular coefficient.
2) You find the angular coefficient of the line that pass through the points (1,1) and (-3,2). It is DeltaY/DeltaX or
m(AB) = (2-1)/(-3-1) = -1/4
3) The coefficient of the perpendicular is the inverse and symmetric of that obtained... so m= 4
4) Finally the equation is y+2 = 4(x-4) or y = 4x -18
or 4x -y -18 =0

Answer 3

(1,1) and (-3,2)

m = (2 - 1)/(-3 - 1)
m = 1/(-3 + (-1))
m = 1/(-4)
m = (-1/4)

Perpendicular
(4,-2), m = 4
-2 = 4(4) + b
-2 = 16 + b
b = -18

ANS : -4x + y = -18