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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