# 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.