3x+4y=12
4y = - 3x + 12
y = -3/4 x + 3; This line has slope equal - 3/4
Perpendicular lines, slope is opposite and reciprocal so slope of new line = 4/3
Passing point (6 , -2)
y + 2 = 4/3(x - 6)
y + 2 = 4/3 x - 8
y = 4/3 x - 10
Answer
Equation: y = 4/3 x - 10