2x+3y=6 can be written in standard form: y=-2x/3+2. This tells us the slope is -2/3. The slope of the perpendicular inverts this and negates the result, so we end up with 3/2. The standard form of the equation of the perpendicular is y=3x/2+b, where b is something we need to find (the y intercept). The point (-3,6) is on the perpendicular so we can write: 6=-9/2+b, so b=6+9/2=21/2. The equation of the perpendicular is y=3x/2+21/2 or 2y=3x+21 or 2y=3(x+7)