Question 416786
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Hi
Using the standard slope-intercept form for an equation of a line y = mx + b
  where m is the slope and b the y-intercept. 
Finding whether the pair of lines is parallel perpendicular or neither
5x+3y=10   OR   y = (-5/3)x + 10/3   m = (-5/3) Green Line
3x-5y=9    OR   y = (3/5)x - 9/5     m = 3/5
Lines are perpendicular (slopes are negative reciprocals, that is (-5/3)*3/5 = -1
{{{drawing(300,300,   -10,10,-10,10,  grid(1),
circle(0, 10/3,0.4),
circle(0,-9/5,0.4),
graph( 300, 300, -10,10,-10,10,0,(-5/3)x + 10/3, (3/5)x - 9/5 ))}}}