Inclination of a Line:
Angle from X-axis to any given non horizontal line is called inclination of line . Here is the inclination where , measured in the 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 formula to find the slope of a line is given by
If a straight line is parallel to X-axis, then its slope is equal to zero i.e. . If the straight line is parallel to Y-axis, then its slope is undefined i.e. .
If the line is parallel to X-axis, then ordinate of each point on the line is a fixed number, so its equation will be , where is some fixed number. If the line is parallel to Y-axis, then abscissa of each point on the line is a fixed number, so its equation will be , where is some 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 straight line with inclination with X-axis.
Here we have the inclination with X-axis, now shall find the slope of straight line using the formula ,