Angle coefficient

We call it angular coefficient straight r the real number m such that:

The angle is counterclockwise oriented and obtained from the positive half axis Ox to the straight r. So we always have . Like this:

  • for (tangent is positive in 1st quadrant)

  • for (tangent is negative in 2nd quadrant)


Determination of the angular coefficient

Let's consider three cases:

a) the angle is known

b) the coordinates of two distinct points of the line are known: THE(xTHE, yTHE) and B(xB, yB)

How (corresponding angles) we have to .

But, m = tg So:

Thus, the angular coefficient of the line passing, for example, through THE(2,3) and B(-2, 5) é:

c) the general equation of the line is known

If a line goes through two distinct points THE(XTHE, YTHE) and B(XB, YB), we have:

Applying Laplace's theorem in the first line, comes:

(YTHE - YB) x + (XB - XTHE) y + XTHEYTHE - XBYB = 0

From the general equation of the line we have:

Overriding these values ​​in we have:

Equation of a line r, known the angular coefficient and a point of r

Be r an angular coefficient line m. Being P(X0, Y0), P r and Q(x, y) any point of r (QQ), we can write:

As an example, let's determine the general equation of the line r that goes through P(1, 2), where m = 3. So we have X0= 1 and Y0= 2. Soon:

y-y0= m (x-x0)
y-2 = 3 (x - 1)
y-2 = 3x - 3
3x - y - 1 = 0

which is the general equation of r.

Next: Line Graphing