4y=5x−8=>y=45x−2
slope1=m1=45 If two lines with slopes m1 and m2 are perpendicular then m1m2=−1.
Then 45m2=−1.
slope2=m2=−54 The equation of the second line is
y=−54x+b This line passes through the point (2,3)
3=−54(2)+b=>b=y=523x The equation of the line which is perpendicular to 4y=5x−8 and passing through (2,3) is
y=−54x+523 Or
5y=−4x+23
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