Lines are something that have been in use by humans since a long time. A variety of applications have been brought into use involving lines. Topics which are mostly mathematically centered have used a good amount of theory involving lines. These topics include trigonometry, geometry, mensuration etc. are some of the topics which involve extensive use of the concept of lines. Now there are different types of lines, the one used mostly is the vertical lines. It is a line which is parallel to the y axis in the Cartesian coordinate plane.

Now this drags us to the point where we try to implicate what a Cartesian coordinate plane is. Well to answer that it is nothing but a coordinate system where different points are represented by the combination of two points. These two points usually are the corresponding x and y coordinate of the position that it holds. Let us try to understand with the help of an example which will provide us a clearer understanding, suppose we have a point with coordinates in the form (3, 7) and we have to represent it on the Cartesian plane. Then we first see the coordinates since it is generally of the form (x, y) then that means the given point has x=3 and y=7. So in order to mark it we first move 3 units on the x axis since x=3 then we move 7 units on the y axis since y=7. In all, first right then up.

The final point at which we arrive is the point where the point is to be marked. This concept is thought of as belonging to the geometry topic but is of immense use everywhere. Topics like trigonometry and mensuration too take rampant use of this concept. Additionally subjects like Physics and chemistry also have extensive use of this topic or whichever topic involves graphs have to use this concept in order to proceed further. The slope of this kind of line is undefined or infinite. Slope here means the tan of the angle that the line substitutes with the horizontal plane. Now since this line is perpendicular to the horizontal or to say it substitutes an angle of 90 degrees. So tan (90°) = infinity. So the slope of this kind of line is said to be undefined or infinity.

So we saw the equation of a horizontal line to be x=k, where k is a constant. Let us have a look at some of the additional equation examples.

- x = 0, it is the equation of the y axis in the Cartesian plane.
- x = 7
- x = 2
- x = 6

Now let us have a look at one more kind of line that there is which is the horizontal line. It is a line which stands parallel to the x axis in the Cartesian coordinate plane. Its equation is of the form y=k, where k is a constant. Let us have a look at some of the additional equation examples.

- y = 0, it is the equation of the y axis in the Cartesian plane.
- y = 8
- y = 3
- y = 1
- y = 6

The slope of a horizontal line is undefined or infinity. Slope here means the tan of the angle that the line substitutes with the vertical plane. Now since a horizontal line is perpendicular to the vertical or to say it substitutes an angle of 90 degrees. So tan (90°) = infinity. So the slope of a horizontal line is said to be undefined or infinity.

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## Conclusion:

Close examination of the content mentioned above surrounding the intricacies of the concept of lines and its types shed light on a lot of crucial information. We come to discover the sheer importance and uses of these lines and their concepts across different topics and subjects. We also learnt the basics of the Cartesian coordinate system.