Question 668181
Perpendicular lines have a negative inverse slope.
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Using 2x -5y = 10 rewritten as y = {{{(2/5)x - 2}}}
The slope is {{{2/5}}}
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The slope of the perpendicular line will be -{{{5/2}}}
Using this slope and the point (3, -1), solve for y-intercept, b.
-1 = -{{{5/2}}}3 + b
Isolate b
b = -1 + {{{15/3}}} = {{{-3/3 + 15/3 = 12/3 = 4}}}
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The linear equation of the perpendicular line is
{{{highlight(y=-(5/2)x + 4)}}}
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Red line:  y = -{{{5/2}}}x + 4
Green line:  y = {{{(2/5)x - 2}}}
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{{{graph(300,200,-10,10,-10,10, (-5/2)x+4, (2/5)x-2)}}}
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