Question 118055
Perpendicular lines have opposite reciprocal slopes.  So we need to find out the slopes of our lines.  If 2x-3y+6=0, then 3y=2x+6 and y=(2/3)x+2, so the slope is 2/3.  So the perpendicular line has a slope of -3/2.  Now we need the x-intercept.  The x-intercept is the point with a y-coordinate of 0.  So going back to the equation y=(2/3)x+2, plugging in a 0 for y gives 0=(2/3)x+2.  So (2/3)x=-2 and x=-3.  So both this line and the perpendicular line have contain the point (-3,0).  So the equation with the point (-3,0) and a slope of -3/2 is the answer.  Using the point-slope form of a line, y-0=(-3/2)(x+3), or y=(-3/2)x-(9/2).  (Or even 3x+2y+9=0)