Is the line y=3 in the Cartesian co ordinate system along the x axis or the y axis?

Expert Answers
durbanville eNotes educator| Certified Educator

The line y=3 is a horizontal line and, is therefore parallel to the x-axis. Whichever x value is appropriate, the y-value will not change. In this case y=3 so whether x = 0 or x = 1 and so on, y remains at 3. The co-ordinates in other words would be (0,3), (1,3), (2.5,3), etc.

The graph reveals all the different potential values of x for y=3 should a vertical line be drawn to cross y=3. 

The line y=3 also serves as an asymptote, wherein as the x value approaches infinity or negative infinity, the graph of the function `y = f(x)` approaches the line.

Ans: In the Cartesian plane, the line y=3 runs parallel to the x-axis.

nav1996 | Student

The line y = 3 in the Cartesian coordinate actually does not run "along" the x-axis nor the y-axis. When graphed, the function y = 3 runs parallel to the x-axis. In order to visualize it more, think of it as a function in which for each x-value, the y-value will always be 3. 

On the Cartesian coordinate system, this would mean that the y-value of the graph never changes, even as the x-values continue to change.

As seen from this graph, the line runs parallel to the x-axis.