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Find the slopes of each line to determine how they compare to each other. The slopes can be found using the form y1 - y2/x1 - x2, like so:
-7 - (-5)/-3 - (-7)  =>  -7 + 5/-3 + 7  =>  -2/4  =>  -1/2  <---This is the slope of L1
-2 - (-6)/-5 - (-7)  =>  -2 + 6/-5 + 7  =>  4/2  =>  2  <--- This is the slope of L2

Lines with slopes that are opposite reciprocals of each other are perpendicular, therefore these lines are perpendicular.