Answer
$y=-5/4x+4$
Work Step by Step
through (0,4), perpendicular to $4x-5y=10$
$4x-5y=10$
$-5y=10-4x$
$(-5y=10-4x)/-5$
$y=-2+4/5*x$
$y=4/5*x-2$
Perpendicular lines have slopes whose product is -1
$-1=4/5*x$
$-5/4=x$
$y=mx+b$
$y=-5/4x+b$
$4=-5/4*0+b$
$4=0+b$
$4=b$
$y=-5/4x+4$