To determine on which axis or line the point [tex]\((0,6)\)[/tex] lies, let's analyze the given coordinates in detail.
1. Coordinate Analysis:
- The point is given as [tex]\((0, 6)\)[/tex].
- The x-coordinate is [tex]\(0\)[/tex].
- The y-coordinate is [tex]\(6\)[/tex].
2. Checking the x-axis:
- Points on the x-axis have a y-coordinate of [tex]\(0\)[/tex].
- Here, the y-coordinate is [tex]\(6\)[/tex], not [tex]\(0\)[/tex].
- Therefore, the point [tex]\((0, 6)\)[/tex] does not lie on the x-axis.
3. Checking the y-axis:
- Points on the y-axis have an x-coordinate of [tex]\(0\)[/tex].
- Here, the x-coordinate is indeed [tex]\(0\)[/tex].
- Therefore, the point [tex]\((0, 6)\)[/tex] lies on the y-axis.
4. Checking the line [tex]\(y = x\)[/tex]:
- Points on the line [tex]\(y = x\)[/tex] have coordinates in the form [tex]\((a, a)\)[/tex], where [tex]\(a\)[/tex] is any real number.
- Here, the point is [tex]\((0, 6)\)[/tex], where the x-coordinate [tex]\(0\)[/tex] is not equal to the y-coordinate [tex]\(6\)[/tex].
- Therefore, the point [tex]\((0, 6)\)[/tex] does not lie on the line [tex]\(y = x\)[/tex].
In conclusion, the point [tex]\((0, 6)\)[/tex] lies on the y-axis.
