For this written assignment, answer the following questions showing all of your work.
1. Determine whether the lines given by the equations below are parallel,
perpendicular, or neither. Also, find a rigorous algebraic solution for each
problem.
A. 3y+4x=12
-6y=8x+1
Rewrite the above equation on the form y = mx + b
3y + 4x =12 -6y = 8x + 1
3y = -4x+12 y = 8x + 1
y = -4x + 12 -6
3 y = -3x - 1
y = -4x + 12 6 6
3 3 y = -4x - 1
y = -4x + 4 3 6
3 Slope of this line = -4
Slope of this line m = -4 3
3
As the slope of both lines are same, we say that 3y +4x =12 and -6y = 8x + 1 are parallel
lines
, B. 3y+x=12
-y=8x+1
Rewrite the above equation on the form y = mx + b
3y + x = 12 -y=8x+1
3y = -x + 12 y = -8x - 1
y = -x + 12
3 Slope of this line = -8
y = -1x + 12
3 3
y = -1x + 4
3
Slope of this line m = -1
3
Since the slopes are Not Equal (Parallel) or the product of slopes -1x – 8 ≠ -1 then the lines
3
are Not perpendicular. Therefore the given lines 3y + x = 12 and -y=8x+1 are neither
parallel nor perpendicular.
1. Determine whether the lines given by the equations below are parallel,
perpendicular, or neither. Also, find a rigorous algebraic solution for each
problem.
A. 3y+4x=12
-6y=8x+1
Rewrite the above equation on the form y = mx + b
3y + 4x =12 -6y = 8x + 1
3y = -4x+12 y = 8x + 1
y = -4x + 12 -6
3 y = -3x - 1
y = -4x + 12 6 6
3 3 y = -4x - 1
y = -4x + 4 3 6
3 Slope of this line = -4
Slope of this line m = -4 3
3
As the slope of both lines are same, we say that 3y +4x =12 and -6y = 8x + 1 are parallel
lines
, B. 3y+x=12
-y=8x+1
Rewrite the above equation on the form y = mx + b
3y + x = 12 -y=8x+1
3y = -x + 12 y = -8x - 1
y = -x + 12
3 Slope of this line = -8
y = -1x + 12
3 3
y = -1x + 4
3
Slope of this line m = -1
3
Since the slopes are Not Equal (Parallel) or the product of slopes -1x – 8 ≠ -1 then the lines
3
are Not perpendicular. Therefore the given lines 3y + x = 12 and -y=8x+1 are neither
parallel nor perpendicular.
