### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Equation of a line in various forms

(i) Slope-intercept form:

is the equation of a straight line whose slope is  and which makes an intercept on the -axis.

Example:

Find the equation of a line with slope and cutting off an intercept   units one negative direction of – axis.

and

(ii) Slope-Point form:

Let a line have slope and let it pass through a point then the equation of the line is given by

Example:

Slope and then equation of line is

(iii) Two-Point form:

A line pass through two given points and . Then the equation of the line is given by

where slope of the line

Example:

Equation of the line is

(iv) Intercept form:

Let line have – intercept and – intercept . Then the equation is

Example:

Equation of the line where is

(v) Determinant form:

Equation of a line passing through and is

Example:

Let and be two points , then equation of the line is

(vi) Perpendicular /Normal Form:

is the equation of the straight line where the length of the perpendicular form the origin   on the line is and this perpendicular makes an angle with positive -axis.

Example:

Here

Equation of the line is

Note:

The normal form of equation is where

and

(vii) General form:

is the equation of a straight line in the general form. In this case, slope of line – intercept , – intercept

Example:

Find slope , – intercept and -intercept of the line

Hence

Slope

-intercept

-intercept

(viii) Parametric Form:

or is the equation of the line in parametric form, where is the parameter whose absolute value is the distance  of any point on the line from the fixed point

The above form is derived from slope-point form of the line

where

Lines Continued:

Consider the equations of lines and   given by

Slopes and   of and are given by   and   respectively.

Case of Parallel Lines:

The lines and are parallel if   or   or

Therefore, we can write equation of   as

Working Rule:

If a line is represented by , the the equation of a line , parallel to , is given by .

If , in the equation of , either or is zero , then also the equation of , parallel to , is given by .

Since in this case, both   and represent lines parallel to the same coordinate axes.

Case of Perpendicular Lines:

The lines represented by   and   being respectively vertical and horizontal are mutually perpendicular.

Now consider a line

We can write the equation of a line perpendicular to , as

The slopes of   and , respectively   and . The product of the slopes being , the lines are  mutually perpendicular .

Working Rule:

To write the equation of , perpendicular to , just interchange the coefficients of and in the equation of and write one of the coefficients by reversin its sign.

Example:

then

Hence

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