A straight line is a curve such that every point on the line segment joining any two points on it lies on it.
If a point moves on a plane in a given direction then its locus is called a straight line and the equation of its locus is called the equation of the straight line.
Every first degree equation in x, y represents a straight line.
When we say that a first degree equation in x, y i.e., ax + by + c = 0 represents a line, it means that all points (x, y) satisfying ax + by + c = 0 lies along a line. Thus a line is also defined as the locus of a point satisfying the condition ax + by + c = 0 where a, b, c are constants.
We can have different forms of the equation of a straight line by assigning the direction of the moving point in various methods. However, these different forms of equation of a line are not independent i.e., one form of equation of a line can be reduce to other form. It follows from the above discussion that ax + by + c = 0 is the general equation of a line.
It should be noted that there are only two unknowns in the equation of a straight line because equation of every straight line can be put in the form ax + by + c = 0 where a, b are two unknowns. Note that x, y are not unknowns. In fact these are the coordinates of any point on the line and are known as the current coordinates. Thus, to determine a line we will need two conditions to determine the two unknowns. In the further discussion on straight line we will find that whenever it will be asked to find a straight line there will always be two conditions connecting the two unknowns.
● The Straight Line