**
Straight line
**

*
General equation of straight
line. Normal vector.
*

*
Equation of straight line with
slope.
*

*
Equation of straight line in
segments on axes.
*

*
Equation of straight line going
through two different points.
*

*
Parametric equation of straight
line.
*

*
Parallelism condition of straight
lines.
*

*
Perpendicularity condition of
straight lines.
*

*
Distance between two points
*
.

*
Distance from point to straight
line.
*

*
Distance between parallel
straight lines.
*

*
Angle between straight lines.
*

*
*

**
A general equation of straight
line:
**

*
Àõ + Âó + Ñ =
*
0 ,

where
*
À
*
and
*
Â
*
aren't equal to zero simultaneously.

Coefficients
*
À
*
and
*
Â
*
are coordinates of
**
normal vector
**
of the
straight line
(
i.e.
vector, perpendicular to the
straight line
). At

*À =*0 straight line is parallel to the axis

*ÎÕ*, at

*Â =*0 straight line is parallel to the axis

*Î Y*.

At
*
*
*
Â
*
0
we
receive
**
an equation of straight line with a slope
**
:

An equation of the straight line,
going through the point (
*
õ
*
_{
0
}
,
*
ó
*
_{
0
}
**
**
) and not parallel to
the axis

*OY*:

*
ó
*
–
*
ó
*
_{
0
}
=
*
m
*
(
*
x
*
–
*
õ
*
_{
0
}
) ,

where
*
m
*
is
**
a slope
**
,
equal to tangent of an angle between the straight line and the positive
direction of the
axis

*ÎÕ*.

At
*
*
*
À
*
0,
*
Â
*
0 and
*
Ñ
*
0
we
receive
**
an equation of straight line in segments on axes
**
:

where
*
a
*
= –
*
C
*
/
*
A
*
,
*
b
*
= –
*
C
*
/
*
B
*
. This line goes through the points (
*
a
*
,
0
) and (
0,
*
b
*
),
i.e. it cuts off
segments
*
a
*
and
*
b
*
long on the coordinate axes.

**
An equation of straight line
going through two different points
**
(

*õ*

_{ 1 },

*ó*

_{ 1 }) and (

*õ*

_{ 2 },

*ó*

_{ 2 }):

**
A parametric equation
of straight line
**
,
going through a point
(

*õ*

_{ 0 },

*ó*

_{ 0 }

**) and parallel to a direction vector (**

*a*,

*b*) of a straight line :

**
**

**
A
parallelism condition of straight lines:
**

1) for lines
*
Àõ
+
Âó
+
Ñ
=
*
0 and
*
D
*
*
õ
+
E
ó
+
F =
*
0 :
*
AE
*
–
*
BD
*
= 0 ,

2) for lines
*
ó
*
=
*
m
*
*
x+ k
*
and
*
ó
*
=
*
p
*
*
x+ q
*
:
*
m
*
*
*
=
*
p
*
.

**
A perpendicularity
condition of straight lines:
**

1) for lines
*
Àõ
+
Âó
+
Ñ
=
*
0 and
*
D
*
*
õ
+
E
ó
+
F =
*
0 :
*
AD
*
+
*
BE
*
= 0 ,

2) for lines
*
ó
*
=
*
m
*
*
x+ k
*
and
*
ó
*
=
*
p
*
*
x+ q
*
:
*
m
*
*
p
*
=
– 1 .

**
A
distance between two points
**
(

*x*

_{ 1 }

*,*

*y*

_{ 1 }

*)*

_{ }and

**(**

*x*

_{ 2 }

*,*

*y*

_{ 2 }

*) :*

**
A distance from a point
**
(

*õ*

_{ 0 },

*ó*

_{ 0 }

**)**

*to a straight line**Àõ + Âó + Ñ =*0 :

**
A distance between
parallel straight lines
**

*Àõ + Âó + Ñ =*0 and

*A õ + B ó + F =*0 :

**
An angle
**
a

*between straight lines:*