Equation of straight lines :
The first-degree equation in x and y is known as a general form of a straight line.
Example – ax + by + c = 0 , where a and b are not both zero at a same time.
x = 0 , Y-axis.
y = 0 , X-axis
x = a , parallel to Y-axis.
Y = b, parallel to X-axis.
The distance of a point (x, y ) from x-axis is |y| and from y-axis is |x|.
Slope = -a/b
Intercept on x-axis :
x = -c/a
Intercept on y-axis:
Put x = 0
y = -c/b
An equation of a line has slope m = tanθ and cutting off an intercept c on Y-axis.
y = x.tanθ + c
y = mx+c
3. Intercept form
An equation of a straight line L and cutting of an intercepts a and b upon axes of X and Y respectively.
x/a + y/b = 1
if the equation of a straight line L is –
a) parallel to X-axis, X-intercept is not defined.
b) parallel to Y-axis, Y-intercept is not defined.
An equation of a line passing through one point and having slope m.
y-y1 = m.(x-x1).
Here m= tanθ
An equation of a straight line passing through two points (x1, y1) and (x2, y2).
y – y1 = [ (y2 – y1)/( x2 -x1 )]( x – x1)
An equation of the straight line at which the perpendicular from the origin is of length p and makes an angle a with the positive direction of the x-axis is –
Then equation of a straight line is: x cos a + y sin a = p
OM = P
An equation of a straight line passing through A( x1, y1 ) and making an angle θ with the positive direction of the x-axis.
In this equation r is the directed distance between the points A( x1, y1 ) and P( x, y ).
x – x1 = r cosθ
x = x1 + r cosθ
y – y1 = r sinθ
y = y1 + r sinθ
So, co-ordinate of any point on the line at a distance r from point A( x1, y1 )
can be taken as ( x1 + r cosθ , y1 + r sinθ )
Hence r is positive for above points A and negative for points below A and 0< θ ≤ 2𝜋