Inclination of a line is a real number as defined below:
(i) If a line is parallel to
– axis or coincides with
-axis then
(ii) If a line is not parallel to -axis then let it intersect
-axis at a point
.
Inclination of
is given by
(iii) Inclination of or
is defined as the inclination of
Note:
If
is the inclination of a line then
.
Parallel lines have same inclination and conversely.
Inclination of perpendicular line differ by
.
Inclination is essentially an angle-measure. The only difference is that inclination can be zero, where as angle-measure can not be zero.
Slope (Gradient) of Non-Vertical Line:
The slope of a non-vertical line is given by , where
is the inclination of the line.
Note:
Inclination
, but slope
.
Slope of a vertical line is not defined.
Slope of a line is positive, zero or negative according as the inclination of the line is less than
, equal to
or greater than
respectively.
It is obvious that slope of a line is the ration of its rise or fall
to its run
A line with positive slope looks like rising where a line with negative slope looks like falling as we move from left to right along the line.
Positive Slope:
Negative Slope:
Zero Slope:
Undefined Slope: