Perpendicular lines have slopes that are negative reciprocals of one another. This equation is:
y = -(3/2)x - 5/2 with slope -3/2
So the slope of the perpendicular line will be 2/3
To find the y intercept we substitute: 4 = (2/3)3 + c or c = 2
So the equation of a perpendicular line passing through point (3,4) is:
y = (2/3)x + 2