The most general equation of a line is of the form: |
![](/TrigoCalc/Line2D/EQ/lineEquation.png) |
(1) |
where A, B and C are any real number and A and B are not both zero. If B ≠ 0 then we can divide
equation (1) by B to obtain the form: |
![Line equation](/TrigoCalc/Line2D/EQ/lineEquationNormal.png) |
(2) |
This is the equation of a line whose slope is: |
![Line slope](/TrigoCalc/Line2D/EQ/lineSlope.png) |
and |
![Line intercept](/TrigoCalc/Line2D/EQ/intercept.png) |
Equation (2) can be normalized to the general form: |
![](/TrigoCalc/Line2D/EQ/lineEquation1.png) |
(3) |
the slope of the line (m) is defined in terms of the inclination |
![Line slope definition](/TrigoCalc/Line2D/EQ/lineSlope1.png) |
(4) |
Note: if the angle α is greater then 90 degrees then the slope is negative.
α (0 - 90) degrees : positive slope |
α (90 - 180) degree : negative slope |
Necessary condition for two lines to be perpendicular to each other is that their slopes fulfill the
condition: |
m1 m2 = − 1 |
(5) |
In order to find the intersection point of two lines we have to solve the system of linear equations
representing the lines. |
A x + B y = −C |
D x + E y = −F |