first thing you have to do is get the lines in y=mx + b form. to do this simply solve for y.
5x + 3y =9 (subtract 5x on both sides)
3y = 9 - 5x finally divide each side by 3
y= (9-5x)/3
3x - 5y =2 (subtract 3x on both sides)
-5y = 2 - 3x (finally divide each side by -5)
y = (2-3x)/-5
these lines are prependicular, they cross at (1.5,.5)