Inclined lines calculator
Line
(mb)
Equation
x + y + = 0
2 points
(x1,y1) ( ) (x2,y2) ( )
Slope, Point
(xp,yp) ( ) Slope = Angle =
Angle from line mb
Degree Radian      Point: ( )
Inclined

lines
Line 1 (m1) Equation
Slope
Angle
Line 2 (m2) Equation
Slope
Angle
line geometry Two lines intersection
Line rotated by an angle θ from a line
Line rotated by an angle ±θ from a given line whose slope is mb
The slope of a given line is:       mb = tan θb     or     θb = tan-1 mb
The angles of the lines which are inclined by an angle θ from the original line are:     θ1 = θb − θ     and     θ2 = θb + θ
Hence the slopes of the lines are: m1 = tan θ1 = tan (θb − θ)
m2 = tan θ2 = tan (θb + θ)
And the inclined lines equations which are passing throught the point
(x0 , y0) are:
y − y0 = m1(x − x0) = tanb − θ)(x − x0)
y − y0 = m2(x − x0) = tanb + θ)(x − x0)
Or expressed by mb
y − y0 = tan(tan-1 mb ± θ)(x − x0) = tanb ± θ)(x − x0)
the plus and minus signs stands for the two lines equations which lies either side of the original line.
Example: find the equation of a line that is inclines by 15 degrees to the right of the line
2x −y + 3 = 0 and is passing through the point (1 , 5).
The slope of the given line is: mb = 2
The angle of the given line is: θb = tan-1 2 = 63.43 degree
The angle of right incline line is: θ1 = 63.43 − 15 = 48.43 degree
The slope of right incline line is: mθ = tan 48.43 = 1.13
Hence the line equation is:
(y − 5) = tan(63.43 − 15)(x − 1)
(y − 5) = 1.13(x − 1)
1.13x − y + 3.87 = 0