Hanuman Chalisa PDF in Hindi 

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ANGLE OF INCLINATION OF A LINE

The angle of inclination of a line is the smallest angle θ which the line makes with the positive direction of x-axis in anticlockwise direction.

In figure angle of inclination of line AB = 135⁰ and in figure angle of inclination of line AB 45⁰.

SLOPE OR GRADIENT OF A LINE

If a line makes an angle θ (θ = 90⁰ ) with the positive direction of x-axis, then tan e is called the slope or gradient of the line. It is usually denoted by m.

SLOPE OF A LINE WHEN COORDINATES ARE GIVEN 

As we know one point can be drawn between two given points and this line are completely determined

Theorem : Slope of the line when joining two points ( X₁ , Y₁) and (x₂ , y₂) are as under ;-

  

EXAMPLE : Slope of the line joining (1, 2) and (3, 7) 

m = 2-7 = 5

                    1-3 = 2

Note : Three points A,B and C are collinear iff slope of AB = Slope of BC.

CONDITION FOR PARALLELISM AND PERPENDICULARITY OD TWO LINES RELATED TO THEIR SLOPES 

1) Condition for parallelism

suppopse m₁ and m₂ are slope of two lines AB and CD that are not parallel to the Y-Axis and making angle a and b with +ve direction of x axis 

if the slope m₁ and m₂ are equeal then both the lines are parallel 

                           m₁+m₂

                           

2) condition for perpendicularity 

suppose m₁ and m₂ are the slope of two line then , 

m₁.m₂ = -1 , or

it alway shows perpendicularity when angle between them is 90⁰ or a right angle 

ANGLE BETWEEN TWO LINES 

            

Slope intercept form of equation of a line

Theorem:- if slope of equation of straight line is m that cut an intercept c on y axis then

                                   Y=mx+c

Equation of straight line in point slope form 

1.line joining two given points (x1 , y1) and (x2 , y2)

    m = y₁ - y₂ or y₂ - y₁

           x₁ - x₂ x₂ - x₁

point slope form

when straight line passes through the point (x₁ , y₁) and make a slope m then equation of line is

y-y₁ = m(x-x₁)

two point form

when line passes through two point (x₁ ,y₁) and (x₂ , y₂) then ,

y-y₁ = y₁ - y₂ (x-x₁)

          x₁ - x₂