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 ,