Answer
Neither parallel nor perpendicular
Work Step by Step
$L_{1}$: $2x-5y=8$
$2x-5y=8$
$2x=8+5y$
$2x-8=5y$
$(2x-8)/5=5y/5$
$2/5*x-8/5=y$
$L_{2}$: passes through (1,4) and (-1,-1)
$m=(4--1)/(1--1)$
$m=5/2$
$y=mx+b$
$4=1*5/2+b$
$4=5/2+b$
$3/2=b$
$y=5/2*x+3/2$
The product of the slopes is 1, so the lines are not perpendicular. The slopes are not the same, so the lines are not parallel.
