Perpendicular lines have slopes that are negative reciprocals of one another.
slope intercept form (y = mx + b) of the first equation will help us find the slope of the first line: where m = slope
5x-4y=10
-4y=-5x + 10
y=-5/-4 x + 10/-4
y=5/4 x -2.5
if the slope of this line is 5/4 then the slope of the perpendicular line is -4/5.
Therefore with the given information we can state the equation of the second line in point slope form (y-y,) = m(x-x,)
the coordinates of (5,12) can are substituted for x, and y,
so the answer is
(y-12) = -4/5(x-5)
I hope this helped and is BRAINLIEST!
Good luck with your studies!
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