Step-by-step explanation:
we need to find the slope of each line.
the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
parallel lines have the same slope.
for a perpendicular line x and y in the slope ratio are put upside down, and the sign is flipped (+ to - and vice versa).
a.
2x - 8y = -24
2x + 24 = 8y
y = 2/8 x + 24/8 = 1/4 x + 3
the slope is 1/4 (always the factor of x).
4x + y = -2
y = -4x - 2
the slope is -4 = -4/1.
this line is therefore perpendicular to the first line.
x - 4y = 4
x - 4 = 4y
y = 1/4 x - 4/4 = 1/4 x - 1
the slope is 1/4.
this line is therefore parallel to the first line.
b.
3x - 9y = 9
9y = 3x - 9
y = 3/9 x - 9/9 = 1/3 x - 1
the slope is 1/3
3y = x + 12
y = 1/3 x + 4
the slope is 1/3.
this line is therefore parallel to the first line.
2x - 6y = 12
6y = 2x - 12
y = 2/6 x - 12/6 = 1/3 x - 2
the slope is 1/3.
this line is therefore parallel to the first line.
