Are these two lines parallel, perpendicular, or neither? Explain. #9x+3y=8#, #3x+9y=8#

1 Answer
Nov 24, 2015

The given lines are neither parallel nor perpendicular.

Explanation:

To check if two lines are parallel or perpendicular it is good to change the equations to form #y=ax+b#

The first line is:

#9x+3y=8#

#3y=-9x+8#

#y=-3x+8/3#

The second line is:

#3x+9y=8#

#9y=-3x+8#

#y=-1/3x+8/9#

From those equations we can see that those lines are neither parallel nor perpendicular

They would be parallel if the coefficients of #x# were equal.

They would be perpendicular if the coefficients of #x# were inverse and opposite numbers (for example #3# and #(-1/3)# or #(-2)# and #1/2#)