Answer
Parallel: Lines a and f
Perpendicular: Lines b and d, lines c and e
Work Step by Step
line a: $y = 3x + 3$
line b: $x = -1$
line c: $y - 5 = 1/2* (x-2)$
line d: $y = 3$
line e: $y + 4 = -2*(x+6)$
line f: $9x-3y =5$
Converting all lines (where possible) to slope-intercept form
lines a, b, and d are already in slope-intercept form (or are horizontal or vertical lines)
C: $y - 5 = 1/2* (x-2)$
$y - 5 = 1/2*x -1$
$y - 5+5 = 1/2*x -1+5$
$y = 1/2*x +4$
E: $y + 4 = -2*(x+6)$
$y + 4 = -2x - 12$
$y + 4 - 4 = -2x - 12 -4$
$y = -2x - 16$
F: $9x - 3y = 5$
$9x - 3y +3y -5= 5+3y -5$
$9x - 5 = 3y$
$3y = 9x-5$
$3y/3 = (9x-5)/3$
$y = 3x - 5/3$
line a: $y = 3x + 3$
line b: $x = -1$
line c: $y = 1/2*x +4$
line d: $y = 3$
line e: $y = -2x - 16$
line f: $y = 3x - 5/3$
Parallel lines have the same slope. Thus lines a and f are parallel ( $m= 3$).
Perpendicular lines have a product of their slopes equal to -1. Thus, lines c and e are perpendicular. Also, lines b and d are perpendicular since the angle made by the two lines is a 90 degree angle (definition of perpendicular).
