Answer
perpendicular
Work Step by Step
$x+3y=9$
$x+3y-x=9-x$
$3y\div3=(-x+9)\div3$
$y=-\underset\uparrow{\frac{1}{3}}x+3$
$\ \ \ \ \ \ $slope
$3x-y=14$
$3x-y+y-14=14+y-14$
$3x-14=y$
$y=\underset\uparrow3x-14$
$\ \ \ \ \ \ \ \ \ \ $slope
The slopes are negative inverse, so the lines are perpendicular.
