Slope of a Line

Inclination of a Line:
Angle from X-axis to any given non horizontal line l is called inclination of line l. Here \alpha is the inclination where 0 < \alpha   < {180^ \circ }, measured in the counter clockwise direction from the positive X-axis to the line l.


slope-of-line

Slope of a Line:
If \alpha is the inclination of a non-vertical straight line l, then its slope or gradient is defined as \tan  \alpha . The slope of a straight line is usually denoted by m, so formula to find the slope of a line is given by

\boxed{m  = \tan \alpha }


If a straight line is parallel to X-axis, then its slope is equal to zero i.e. m = \tan {0^ \circ } = 0. If the straight line is parallel to Y-axis, then its slope is undefined i.e. m = \tan {90^ \circ } = \infty .
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 y = a, where a 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 x = a, where a is some fixed number.
Let {m_1},{m_2} be the slopes of the lines {l_1},{l_2} respectively.
(i) The lines {l_1} and {l_2} are parallel if and only if {m_1} = {m_2}
(ii) The lines {l_1} and {l_2} are perpendicular if and only if {m_1} \times  {m_2} =  - 1

Example: Find the slope of straight line with inclination {60^ \circ } with X-axis.
Here we have the inclination \alpha  =  {60^ \circ } with X-axis, now shall find the slope of straight line using the formula m = \tan \alpha ,

m =  \tan \alpha  = \tan {60^ \circ } = \sqrt  3

Comments

comments