Place the equations in the slope intercept form y=mx + b. m is the slope.
Parallel lines have equal slopes, perpendicular lines have slopes that are the negative reciprocal of each other. That means if the slope of the first is x then the slope of the second is -1/x. In other words, the negative reciprocal means flip it and make it negative of what it was.
5x - 6y = 19
Subtract 5x from both sides.
-6y = -5x + 19
Divide both sides by -6
y =(5/6)x-19/6
The slope of that line is 5/6.
6x + 5y = -30
Subtract 6x from both sides.
5y = -6x - 30
Divide both sides by 5
y = (-6/5)x - 6
The slope is -6/5.
5/6 flipped over and negated is -6/5. They are negative reciprocals of each other. Therefore the lines are perpendicular.
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