STRAIGHT LINES
1. EQUATION OF STRAIGHT LINE
Every linear equation in two variable x and y always represents a straight line eg. 3x + 4y = 5
General form of straight line is given by ax + by + c = 0
(1) Equation of x-axis : y = 0
(2) Equation a line parallel to x axis at a distance ‘a’ from it is y = a
(3) Equation of y-axis : x = 0
(4) Equation of a line parallel to y axis at a distance ‘a’ from it is x = a
2. SLOPE
The slope of a line is equal to the tangent of the angle which it makes with the positive side of x-axis and it is
generally denoted by m.
Thus if a line makes an angle with x-axis then its slope = m = tanθ
y y
o ) x
x
o
y 2 y1
The slope of a line joining two points (x1, y1) and (x2 , y2) is given by m = x x
2 1
a
The slope of a line ax + by + c = 0 is
b
Note :
(i) Slope of x axis or a line parallel to x axis is tan 0° = 0
(ii) Slope of y axis or a line parallel to y axis is tan 90° =
3. DIFFERENT FORMS OF THE EQUATION OF STRAIGHT LINE
3.1 Slope intercept form :- y = m x + c
Where ‘m’ is the slope of the line and ‘c’ is the length of the intercept made by it on y axis
3.2 Point Slope form : The equation of a line with slope m and passing through a point (x1,y1) is y– y1= m (x – x1)
3.3 Two point form : The equation of a line passing through two given points ( x1 , y1) and (x2 , y2) is
y 2 y1
y – y1 = x x1
x 2 x1
3.4 Intercept form : The equation of straight line which cuts off intercepts a and b on the axes of x and y respectively
x b
is 1
a b
3.5 Normal (Perpendicular) form of a line
x cos + y sin = p is the equation of a straight line on which the length of the perpendicular from the origin
is p and is the inclination of the perpendicular with positive direction of x-axis.
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1. EQUATION OF STRAIGHT LINE
Every linear equation in two variable x and y always represents a straight line eg. 3x + 4y = 5
General form of straight line is given by ax + by + c = 0
(1) Equation of x-axis : y = 0
(2) Equation a line parallel to x axis at a distance ‘a’ from it is y = a
(3) Equation of y-axis : x = 0
(4) Equation of a line parallel to y axis at a distance ‘a’ from it is x = a
2. SLOPE
The slope of a line is equal to the tangent of the angle which it makes with the positive side of x-axis and it is
generally denoted by m.
Thus if a line makes an angle with x-axis then its slope = m = tanθ
y y
o ) x
x
o
y 2 y1
The slope of a line joining two points (x1, y1) and (x2 , y2) is given by m = x x
2 1
a
The slope of a line ax + by + c = 0 is
b
Note :
(i) Slope of x axis or a line parallel to x axis is tan 0° = 0
(ii) Slope of y axis or a line parallel to y axis is tan 90° =
3. DIFFERENT FORMS OF THE EQUATION OF STRAIGHT LINE
3.1 Slope intercept form :- y = m x + c
Where ‘m’ is the slope of the line and ‘c’ is the length of the intercept made by it on y axis
3.2 Point Slope form : The equation of a line with slope m and passing through a point (x1,y1) is y– y1= m (x – x1)
3.3 Two point form : The equation of a line passing through two given points ( x1 , y1) and (x2 , y2) is
y 2 y1
y – y1 = x x1
x 2 x1
3.4 Intercept form : The equation of straight line which cuts off intercepts a and b on the axes of x and y respectively
x b
is 1
a b
3.5 Normal (Perpendicular) form of a line
x cos + y sin = p is the equation of a straight line on which the length of the perpendicular from the origin
is p and is the inclination of the perpendicular with positive direction of x-axis.
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