Question 927135
the standard slope-intercept form for an equation of a line is 
{{{y = highlight_green(m)x + highlight(b)}}}  where m is the slope and b the y-intercept.  
.....
2x-3y = 9  0r  {{{y = highlight_green(2/3)x - highlight(3)}}} (Green)
New perpendicular Line:  m = -3/2
........
***Using point-slope form, {{{y - y[1] = highlight_green(m)(x - x[1])}}}P(4,6)
y - 6 = (-3/2)(x - 4)
y = (-3/2)x + 12  (Blue)
0r
3x + 2y = 24

{{{drawing(300,300,   -10,10,-10,10,   
 grid(1),
circle(4, 6,0.4),
circle(0,-3,0.4),
graph( 300, 300, -10,10,-10,10,0, (2/3)x -3, -1.5x+12))}}}