# The Slope of a Line

__Inclination of a Line__**:**

The angle from the X-axis to any given non horizontal line is called the inclination of line . Here is the inclination where , measured in a counter-clockwise direction from the positive X-axis to the line .

__Slope of a Line__**:**

If is the inclination of a non-vertical straight line , then its slope or gradient is defined as . The slope of a straight line is usually denoted by , so the formula to find the slope of a line is given by

If a straight line is parallel to the X-axis, then its slope is equal to zero, i.e. . If the straight line is parallel to the Y-axis, then its slope is undefined, i.e. .

If the line is parallel to the X-axis, then the ordinate of each point on the line is a fixed number, so its equation will be , where is a fixed number. If the line is parallel to the Y-axis, then the abscissa of each point on the line is a fixed number, so its equation will be , where is a fixed number.

Let be the slopes of the lines respectively.

**(i)** The lines and are parallel if and only if

**(ii)** The lines and are perpendicular if and only if

__Example__**:** Find the slope of a straight line with inclination with the X-axis.

Here we have the inclination with the X-axis, now we shall find the slope of the straight line using the formula ,