Concept:Two lines are perpendicular when the product of their slopes equals −1.Explanation:Write the given line in the form y=mx+c.Starting from 3x+2y+4=0:2y=−3x−4.Divide through by 2:y=−23x−2.So the gradient of the given line is m1=−23.For perpendicular lines, m1×m2=−1.Therefore, m2=m1−1=−23−1=32.The required line passes through (2,3) with gradient 32.Using y−y1=m(x−x1):y−3=32(x−2).Multiply through by 3:3y−9=2x−4.Add 9 to both sides:3y=2x+5.Answer:3y=2x+5