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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
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