### 1. General type of equation of a line

The equation of type: A** x + By + C = 0 is c**alled a

**general type equation of a line.**

Properties:

1. If** A = O**, we get the equatio

**0, ie y**

*n By + C =***which is a line parallel to the x-a**

*= – C / B,***is, at a distance – C /**

*x**om the coordinate origin.*

**B fr**2. If ** B = O**, the equation is reduced

**= 0, ie**

*to Ax + C***A which is a line parallel to the y-a**

*x = – C /***x**is, at a distance – C

*rom the coordinate origin.*

**/ A f**3. If * B = 0, C = 0*, the line equation is reduced to the for

**= 0, ie x**

*m Ax***0. It coincides with the y-axis and represents its equation.**

*=*4. If A* = 0, C = 0,* the equation of a line is reduced to the

*= 0, ie*

**form By***0. The line coincides wit*

**y =****the x-axis and represents its equation.**

*h*### 2. Explicit kind of equation of a line

The equati* on у = kx *+ b, where k

*is called*

**= tg а,****an equation of a line in explicit form**(fig. 4).

The numb** er** k is called the coefficient of the direction of the lin

*and the b-segment that the line intersects on*

**e,****the u-axis.**

### 3. Segment type equation of a line

The equation of a line in segmental form is:

in which** a** an

**b are segments that intersect the lines on the coordinate axes x**

*d***nd**

*a***respectively (fig. 5).**

*y,*

Fig.5

### 4. Normal type equation of a line

The normal type of equation of a line given in general is

in which the sign before the root is opposite to the sign before the coefficient* *C.

### 5. Equation of lines through one and two points

The equation of a line that passes through a given point* M (x₁, y₁)* and has a coefficient of directi

**k reads:**

*on***y – y₁ = k (x – x₁)**

The equation of a line passing through two given points M** Z (x₁, y₁)** an

**) has the following form:**

*d M₂ (x₂, y₂*### 6. Distance from point to line

The distance from the po** int M (x₀, **y₀) to the li

**0 is calculated by the formula:**

*ne Ax + By + C =***7. Angle between two lines**

The angle between the li** nes** l₁,

**d l₂ (Fig. B) is determined by the formula:**

*an*where k₁,* and *k₂

**coefficients of the directions of the lines**

*are***d**

*l₁ an***, respectively.**

*l₂*

From formula (1) are obtained the conditions for parallelism and normality of two lines. Thus, * l₁ || l₂*, if

*if*

**k₂ = k**₁,**l₁⊥l₂**

*1 + k₁k₂ = 0*