Yes
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It is x = 0.
When x = 0, the point that has (0, y) coordinates will be on the y-axis for any y.
The x-coordinate of any point on the y-axis is 0. The y-axis is a line perpendicular to the x-axis. Any point on a line perpendicular to the x-axis has the same x-coordinate. The y-axis is the line perpendicular to the x-axis through 0, and has the equation x = 0; similarly, the x-axis is the line perpendicular to the y-axis through 0 and has the equation y = 0.
Yes, it is.
On the Cartesian plane the y axis crosses the x axis at the point of origin which is at (0, 0)