Question 79648
2X-3Y=12
-3Y=-2X+12
Y=-2X/-3+12/-3
Y=2X/3-4 THIS (RED) LINE HAS A SLOPE(m) OF 2/3.
FOR A LINE TO BE PERPENDICULAR TO THIS LINE THE SLOPE MUST BE THE NEGATIVE RECIPRICAL OF THIS SLOPE. THUS THE NEW SLOPE IS -3/2.
NOW WE SUBSTITUTE THE POINTS (4,3) FOR X & Y AND USING THE NEW SLOPE (-3/2) WE SOLVE THE LINE EQUATION [Y=mX+b] FOR b THE Y INTERCEPT.
3=-3/2*3+b
3=-9/2+b
b=3+9/2
b=3+4.5
b=7.5 THE Y INTERCEPT.
THUS THE EQUATION IS 
Y=-3X/2+7.5 (THE GREEN LINE).
{{{ graph( 300, 300, -10, 10, -10, 10, y = 2x/3 -4, y = -3x/2 +7.5) }}} (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = 2x/3 -4 and y = -3x/2 +7.5). 
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solved the first one. now see if you can handle the rest. :)