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1800-102-2727You may have noticed various objects in your surroundings such as the edge of a table, pen, edge of a notebook and many more objects. They have something in common that is all of them are lines. A line is a one-dimensional shape with zero thickness but length can extend in both directions. Basically, it is a combination of various points which are moving in opposite directions and when these points come too close together they form a line. So, let’s understand this interesting topic in this article.
Table of Contents
A group of points which are moving in a straight path but in opposite directions forms a Line. It has no breadth, no depth (curvature) and no termination means ‘it will not end’ so it keeps moving in a straight path endlessly in opposite directions.
A line is said to be a line segment when it has two fixed endpoints. Line segment is a part of line. The length of the line segment is always constant, which is the distance between the two endpoints. Below shown is a line segment XY.
A line is said to be ray when it has a fixed starting point but no endpoint. It can extend infinitely in one direction. Since a ray has no endpoint so we cannot measure its length.
For example,
Sunray is an example of a ray. The Sun is the starting point or point of origin and its ray extends indefinitely.
The different types of lines are:
They are the part of geometry or we can say that they are the foundation of geometry.
Now, let’s understand each one of them in brief
Type of Line |
Definition |
Diagram |
Horizontal Line |
A line which moves in a straight path from left to right and vice-versa or a line which is parallel to the X- axis is a Horizontal Line. |
|
Vertical Line |
A line is said to be vertical when it is perpendicular to the X- axis. |
|
Parallel Lines |
Two lines are said to be parallel when no two lines coincide or meet each other at any point.The distance between parallel lines is constant everywhere. |
|
Perpendicular Lines |
When two lines intersect each other and form an angle of 900 or make a right angle, then they are said to be perpendicular Lines. |
|
Intersecting Lines |
When two lines meet at any point or cross each other at any point then they are said to be interesting lines. |
|
We represent the general equation of a line in two variables of one degree as
Ax+By+C=0
Where A and B should not be zero simultaneously; and A, B, and C are the real numbers.
The general equation of a line is also known as a linear equation in two variables.
For example:
2x+6y-3=0, where A=2, B=6 and C=-3
In this form, the line is passing through a point (x0,y0) and the slope is m then the equation of the line is given by:
In this form, the line passes through two points say (x1,y1) and (x2,y2) then the equation of line will be given as
In this form, a line with slope m cuts the y-axis at a distance c from the origin. The distance is called the Y-intercept of the line. The line always passes through the point(0,c), therefore by slope-intercept form, the equation of the line will be given as
In this form, the line makes x-intercepts a and y-intercepts b on axes and meets the x-axis at (a,0) and the y-axis at (0,b). Now, by two-point form i.e.,
By putting the value, we get
By rearranging the equation, we get
This is the intercept-form.
Solution: The equation for the x-axis is y=0 and for the y-axis is x=0.
Solution: We have value of the slope i.e., m=5 and (x0,y0) = (2,1)
Now, by using
Solution: Here, the line is passing through (1,2) and (-4,6)
Now,
Solution: The given equation is 2x+y=10
Now,
Hence, the y-intercept is 2.
Solution: We have value of the slope i.e., m=2 and (x0,y0) = (1,4)
Now, by using
A line is a one-dimensional figure with no endpoints.
The slope of two parallel lines is equal.
The slope of a line is zero only when the line is parallel to the x-axis or the line itself is the x-axis.
No, Lines do not have endpoints. Although line segment has 2 end points and ray has 1 end point.