Answer:
The correct option is 2.
Step-by-step explanation:
The slope of two parallel lines are equal.
The slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is slope and b is y-intercept.
In option 1, the equation of lines are
![y=9](https://tex.z-dn.net/?f=y%3D9)
![x=18](https://tex.z-dn.net/?f=x%3D18)
The first line is a horizontal line and the second line is a vertical line. Therefore they are not parallel line. Option 1 is incorrect.
In option 2, the equation of lines are
![y=4x+9](https://tex.z-dn.net/?f=y%3D4x%2B9)
![y=4x-9](https://tex.z-dn.net/?f=y%3D4x-9)
By using the slope intercept form of a line, the slope of first line is 4 and the slope of second line is 4.
Since the slope of both lines are same, therefore both lines are parallel. Option 2 is correct.
In option 2, the equation of lines are
![y=5x+15](https://tex.z-dn.net/?f=y%3D5x%2B15)
![y=-5x+15](https://tex.z-dn.net/?f=y%3D-5x%2B15)
By using the slope intercept form of a line, the slope of first line is 5 and the slope of second line is -5.
Since the slope of both lines are not same, therefore both lines are not parallel. Option 3 is incorrect.