Straight Line

 

Any equation of first degree of the form Ax + By + C = 0, where A, B, C are constants always represents a straight line (at least one out of A and B is non zero).

Slope

Slope Intercept From:

Intercept Form:

x intercept = a

y intercept = b 

Slope point form

Equation:

y – y₁ = m(x – x₁), where (x₁, y₁) is a point on the straight line.

Illustration:

Equation of line in figure (ii) is x = 3, because x-co-ordinate of each point on the line is 3.

Equation of line in figure (iv) is y = 2, because y-co-ordinate of each point on the line is 2.

Although every line satisfied the above given basic definition, a line can be represented in many forms, some of which are given hereunder.

Let there be two points A(x₁, y₁) and B(x₂, y₂) in a co-ordinate plane. If any point P(x, y) lies on the line joining A and b then m = tan θ = y–y₁/x–x₂ = y₂ – y₁/x₂ – x₁,  (see figure given below).

 y – y₁ = y₂ – y₁/x₂ – x₁ (x – x₁) which is the equation of the given line. Equation of line can also be written as

 y – y₂ = y₂ – y₁/x₂ – x₁ (x – x₂) or  = 0.

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