Question 309086
(6,-9);
2x+5y=9
5y=-2x+9
y=-2x/5+9/5  This line has a slope=-2/5. (red line)
A perpendicular line will have a slope=5/2 or 2.5.
-9=2.5*6+b
-9=15+b
b=-9-15
b=-24 is the Y intercept.
y=2.5x-24 (green line).
{{{ graph( 300, 300, -6, 15, -25, 10, -2x/5 +9/5 , 2.5x -24) }}} (graph 300x300 pixels, x from -6 to 15, y from -25 to 10, of TWO functions -2x/5 +9/5 and 2.5x -24). 
Solution (8.89,-1.75)