The general equation of a line is
y = mx + c where m is the slope
The product of the slopes of two perpendicular lines is -1 while the slopes of 2 parallel lines are equal
Considering the lines
y= -1/2x +7 and -x -2y=24
The slope of the first is -1/2
Considering the second
-x - 2y = 24
-2y = x + 24
Divide both sides by -2
y = -1/2 x - 12
the slope of the second also is -1/2
Since the slopes are equal, the lines are parallel