SOLUTION: Determine whether the following lines are parallel, perpendicular, or neither. 6x − 9y = 12 4x − 6y = 18

Algebra ->  Linear-equations -> SOLUTION: Determine whether the following lines are parallel, perpendicular, or neither. 6x − 9y = 12 4x − 6y = 18       Log On


   

Question 203999: Determine whether the following lines are parallel, perpendicular, or neither.
6x − 9y = 12
4x − 6y = 18
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given: system%286x+-+9y+=+12+%28red%28EQN1%29%29%2C4x+-6y+=+18%28red%28EQN2%29%29%29

Transforming each given line to Slope-Intercept Form,red%28y=mx%2Bb%29
red%28EQN1%29:
6x-9y=12 ---> 6x-12=9y ---> %286x-12%29%2F9=cross%289%29y%2Fcross%289%29
y=%286%2F9%29x-12%2F9
y=%282%2F3%29x-4%2F3

red%28EQN2%29:
4x-6y=18 ---> 4x-18=6y ---> %284x-18%29%2F6=cross%286%29y%2Fcross%286%29
y=%284%2F6%29x-18%2F6
y=%282%2F3%29x-3

*The Slope=m of red%28EQN1%29, y=%28highlight%282%2F3%29%29x-4%2F3 is the same as the one for red%28EQN2%29, y=%28highlight%282%2F3%29%29x-3.

Therefore, the two lines are PARALLEL.

---> red%28EQN1%29; green%28EQN2%29

Thank you,
Jojo