# Slope of a Line

Slope (or gradient) of a line is defined as the tangent of the angle which a line makes with +ve X-axis. It is denoted by m.    m = tan

Note:
1.  m can be defined as tan  for    0     &       â‰  /2.
2.  the slope of a line parallel to X-axis = 0 perpondicular to X-axis is undefined.

Slope of a line passing through two given points:

Let the two points be A () and B ().

Slope of line L = m = tan

Ã°        ()
Acute angle between two lines  of given slope

Slope of

Slope of

If  is the acute angle between  then:

tan  =

If is parallel to

If is perpendicular to

# Intercepts of a Line

The line L cuts X and Y axes in A and respectively.

X-intercept of L = OA = a

Y-intercept of L = OB= b

X-intercept will be negative if L intersects â€“ve X-axis and Y-intercept will be negative if L intersects â€“ve Y-axis

If L is parallel to X-axis, X-intercept is undefined and

If L is parallel to Y-axis, Y-intercept is undefined.

# Equation of a line in various forms

### 1.  Equation of line L of slope m and cutting off an intercept b on Y-axis:

Any point P (x, y) on line L satisfies the following:

tan  = m =

Ã°   is the equation line L.

This is also known as slope â€“ intercept form.
2.  Equation of line L of slope m and passing through a given point:

Any point P(x, y) on line L satisfies the following:

Slope = m =

is the equation of line L.

This also known as point â€“ slope form.
3.  Equation of line L passing through two given point:

Any point P(x, y) on line L satisfies the following:

Slope of PA =     & slope of AB =

As PAB is straight line:

slope of (PA) = slope of (PAB)

is the equation of line .

In the determinant form it is given as:

= 0

This is also known as two â€“ point form.