Today we are going to discuss about the equation of line. First of all we should know about line. A line is a basic concept of elementary geometry in which the straight line is basically a joint or we can say the shortest path between two points. A line may have several points and the end and start points of a line are included into line segment. The ends of a line can be shown by arrows.  Here to get the Equation of Line we must know the slope and the points of a particular line. For this we use the point slope form.
   y = m*x + c
Here in the above equation y and x are the points or coordinates of line and m is the slope of line and c is y intercept.
If a line passes thorough the origin then the y intercept of the equation becomes 0 i.e. c = 0.
   y = m*x
To find m and c:
1. For c that is y intercept  we only see the line where it crosses the y axis on a graph.
2. For m that is the slope we need to do some calculation:
m = change in y / change in x
An equation for a straight line is:
    y – y1 = m(x – x1)
here the above equation is the equation of line with slope m and passing through points (x1, y1).
In this case to find slope m = (y – y1) / (x – x1)
If we write the equation of a line in standard form then the equation will become:
    Ax + By + C =0
where A, B, C are the constants and (x, y) are points trough which line passes.
If a line is parallel to y axis then the equation of line become:
    x = a 
When Line is parallel to y axis then it is called Vertical line.
If a line is parallel to x axis then it is known as horizontal line and then the equation of horizontal line is :
    y = c
Now here I will tell you the relation between slope and a parallel line:
1. If two lines which are not vertical but are parallel to each other then both have the same slope.
2. If we have two distinct lines which are not vertical but having same slope then these lines are parallel to each other.
3. If two lines are vertical then they are definitely parallel to each other.
Now to understand the concept more of the lines let’s take some examples:
1. Write an equation of the line with slope -4 and passing through (3, 4).
y - y1 = m*(x – x1)
y – 3 = -4*(x - 4)
y -3 = -4x + 16
y + 4x = 19 that is the equation of the line.
2. Find slope of a line passing through (1, 4) and (3, 2).
m = (y – y1) / (x – x1)
m = (2 - 4) / (3 - 1)
m = -2 / 2
m = -1
So here we learnt how to find equation of line.   

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