Exercise 21 Page 246

Lines are parallel if their slopes are identical and perpendicular if their slopes are negative reciprocals. Any other relationship between the lines would be neither parallel nor perpendicular. Let's write each equation in slope-intercept form, highlighting their slopes.

Given Equation	Slope-intercept form	Slope
$y = - 6 x + 8$	$y = - 6 x + 8$	$m_{1} = - 6$
$3 x + \frac{1}{2} y = - 3$	$y = - 6 x - 6$	$m_{2} = - 6$

Since the lines have equal slopes, we can conclude that they are parallel. This corresponds to option F.