﻿ Inclined lines calculator
 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) = tan(θb − θ)(x − x0) y − y0 = m2(x − x0) = tan(θb + θ)(x − x0)
Or expressed by mb
 y − y0 = tan(tan-1 mb ± θ)(x − x0) = tan(θb ± 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