grandh01 wrote:Is line l parallel to the y-axis?
(1) The equation of line l is x = 4.
(2) The points (4. 2) and (4, - 5) are
on line l .

For a line to be parallel to the y-axis we need either 1 of 2 things.
1. The equation of the line needs to be x= some number or 2. The slope needs to be undefined (or vertical).

Lets look at the statements:

1. x=4. This is sufficient for reasons stated above. You can also visualize this. Draw the line x=4 and you will see that it is indeed parallel.

2. (4, 2) and (4, - 5). If you plot these points you see that the slope is undefined as it is a vertical line. This is also sufficient.

The correct answer is D
Let me know if this helps

My 0.02$

a) If any two points have the same X coordinate, then the line joining these points is parallel to Y-axis.
b) If any two points have the same Y coordinate, then the line joining these points is parallel to X-axis.
c) If the equation of the line is in the form X = Constant, then the line formed by the equation is parallel to Y-axis.
d) If the equation of the line is in the form Y = Constant, then the line formed by the equation is parallel to X-axis.
e) Take a few minutes to plot graphs of the lines X = 4, Y = -3 and the lines joining the points (4,3),(4,-5) and (3,-4),(2,-4).