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the equation of line L1 is 2y-5x-8=0 and line L2 passes through the points (-5,0) and(5,-4). show that the two lines are perpendicular

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If they are perpendicular, you know that their slopes must be negative reciprocals of each other.
You also know that the slope of L1 is 5/2.
Show the slope for L2 is -2/5.

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