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# Line

Top
 Sub Topics A Line is a shortest path between the two points that is straight, infinitely long and thin. In the coordinate plane, the location of a line is defined by the points whose coordinates are known and through which the line passes to an infinitely long distance in both the direction. There are no end points in case of line. A Ray joining which is used to join two points is also known as a line, it is a basic concept of elementary Geometry. Here we differentiate two words line and Line Segment. In the Line Segment the end points are included, and in case of line there is no endpoint. If two distinct lines ‘A‘ and ‘B’, these two lines are intersects each other or both lines are parallel to each other. The two lines which intersect each other have a unique Point or represent a unique point i.e. the point of Intersection. And the intersection point lies on the lines. In case of Parallel Lines there are no common points. Let you have 5 lines, than every line divides the line into two parts, which is known as rays. A piece of line is known as ray, which have only one end point. Rays are used in defining the angles. The line which does not have any end is known as line segment. The line in geometry is the basic design tool. A line has length, width etc. It suggested a direction through which we can find the path easily. If we have a line and which is not straight, then the line usually known as a curve or arc. In the plane geometry, line is used to indicate the Straight Line and the object which is straight, infinity times long are also known as line. A geometry line is always in one dimensional; its width is always zero. If we draw a line with the help of pencil then it shows that the pencil has a measurable width.

## Equation of a Line From Two Points

According to the theorem of Geometry, if two points lies in a plane then there is exactly one line that passes through the two points. So, to write line equation we need two points. The equation of line can be written as,
y = mx + c
where,
'x' and 'y' are two vertices.
'm' is Slope.
'c' is y-intercept.

To calculate the line equation, we have to find value of the slope 'm' first and then we put value of 'm' in the equation. To calculate the slope the below given steps are to be followed:
1. First we subtract old value of 'y' from new value of 'y'.
2. Then we subtract old value of 'x' from new value of 'x'.
3. Now divide above differences.
We write slope by the equation as,
m = $\frac{change \ in \ y-coordinates}{change \ in \ x-coordinates}$
Use this value in the Straight Line equation.

Example:
Find the equation of the line that passes through the points (1,3) and (3, 6) ?
m = $\frac{change \ in \ y-coordinates}{change \ in \ x-coordinates}$
m = $\frac{6-3}{3-1}$
m = $\frac{3}{2}$
Now the equation of the line becomes,
y = mx + c
y = $\frac{3}{2}$x + c

## Straight Line Components

Line or the straight line can be used to represent basic Position of an object such as height, width and length of an object. When an object is placed in two dimensional space then Straight Line is used to measure height and length of this object. When an object is placed in three dimensional space then its height, length and the width are calculated using straight line.

If we talk about line in Geometry coordinate system then we represent line by equation y = mx + c. This linear equation defines straight line in the Cartesian plane. Here the components of the straight line are the coordinates (x, y), slope 'm' and y- intercept 'c'. These are three components which are used in straight line equation.

Straight line equation in two dimensional space can be written as,
y = mx + c
where,
'x' is the independent variable which can be represented by the function y = f(x).
'c' is the Point of y- intercept of straight line.
'm' is the Slope of line.
m = $\frac{change\ in\ y-coordinates}{change\ in\ x-coordinates}$

Straight line equation in three dimensional can be written as,
X = x + ap
Y = y + bp
Z = z + cp
Here x, y and z are components of line. They are Functions of the independent variable 'p'.