Question 61558
Perpendicular lines have slopes that are negative reciprocals of each other. 
Line # 1= 2x-3y=6 [re-write in the slope-intercept form by solving for y]
y=mx+b [slope-intercept form]
-3y=2x+6
y=-2/3-2
m=-2/3
.
Line #2 m=3/2 [the negative reciprocal of line #1.
y=mx+b [plug-in the point (0, 2) and the slope and solve for b]
2=(3/2)(0)+b
2=b
so, line # 1: y=(3/2)x+2
Graphing:
{{{ graph( 300, 200, -6, 5, -10, 10, (3/2)x+2, (-2/3)x-2) }}}