Two lines are parallel if they have the same slope.
To determine the slope of a line easily we can write it in the slope intercept form as y = mx + c, where m is the slope.
- 2y - 6x - 2 = 0
=> 2y = 6x + 2
=> y = 3x + 2/3
The slope is 3
- -3y + 9x +3 = 0
=> 3y = 9x + 3
=> y = 3x + 1
The slope is 3. As the slope of the lines is equal they are parallel.
To determine if two lines are parallel or not, we need to find the slope for each line.
If the slopes are equal, then the lines are parallel.
First we will need to rewrite the equations of the lines into the slope form y= mx + b such that m is the slope.
For equation (1):
2y - 6x -2 = 0
==> 2y= 6x +2
==> y= 3x +1
==> Then the slope is m1= 3...........(1)
For equation (2):
-3y + 9x +3 = 0
==> -3y = -9x -3
==> y= 3x + 1
==> m2= 3 ............(2)
Then we notice that the equations of the lines are the same. Then the lines are parallel.