### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
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

# Inclination of a line

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Inclination of a line is a real number as defined below:

(i) If a line is parallel to – axis or coincides with -axis then

(ii) If a line is not parallel to -axis  then let it intersect -axis at a point .

Inclination of is given by

(iii) Inclination of   or   is defined as the inclination of

Note:

If   is the inclination of a line then .

Parallel lines have same inclination and conversely.

Inclination of perpendicular line differ by .

Inclination is essentially an angle-measure. The only difference is that inclination can be zero, where as angle-measure can not be zero.

The slope of a non-vertical line is given by , where  is the inclination of the line.

Note:

Inclination ,  but slope .

Slope of a vertical line is not defined.

Slope of a line is positive, zero or negative according as the inclination of the line is less than , equal to or greater than respectively.

It is obvious that slope of a line is the ration of its rise or fall to its run

A line with positive slope looks like rising where a line with negative slope looks like falling as we move from left to right along the line.

Positive Slope:

Negative Slope:

Zero Slope:

Undefined Slope:

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