Different forms of the straight lines:

Slope intercept form:

Equation of a line whose slope is m (m = tanq) and which cut an intercept c on the y- axis (that is which passes through point (0, c) is given by y = mx + c.

Intercept form:                        

The equation of the line which cuts off intercepts a and b on x-axis and y-axis respectively is given by x/a +y/b = 1.     

Hence intercept of a straight line on x-axis can be found by putting y = 0 in the equation of the line and then finding value of x. Likewise intercept on y-axis can be found by putting x = 0 in equation of the line and then finding the value of y.

Normal Form:

The equation of straight line upon which length of perpendicular from the origin is p and perpendicular makes an anglewith the positive direction of x-axis which can be given by    

xcosα + ysinα = p

Note: In the normal form of equation of a straight line p is taken as positive and is measured from positive direction of the x-axis in the anticlockwise direction between 0 and 2.

Note: In normal form x cosα+y sinα=p, p is always taken positive.

Point-slope form: The equation of the line passing through the point (x₁, y₁) and having slope m is given by 

.

Two points form: The equation of a straight line passing through 2 given points (x₁, y₁) and (x₂, y₂) can be given by         

Note: Slope of line passing through 2 points (x₁, y₁) and (x₂, y₂) can be given by 

Parametric form:

The equation of line passes through a given point P(x₁, y₁) and makes a given angle q with the positive direction of the x-axis is given by  

where r is distance between the variable point Q  (x, y) and the fixed point P(x₁, y₁).

• Any point on line will be of the form (x₁ +  rcosθ, y₁  +  rsinθ). For the different values of r, we will get different points on line
• Here |r| will gives the distance of the point Q from the fixed point P(x₁, y₁).
• If P(x₁, y₁) is any point on the line which makes an angleq with positive direction of x axis, then there will be 2 points on the line at a distance r from P(x₁, y₁). One will be upward relatively if r is taken positive and other will be downward relatively if r is taken negative.

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