Maths > Straight Lines > 1.0 Definition
Straight Lines
1.0 Definition
2.0 Condition of collinearity of three points
3.0 Equation of a straight line in various forms
3.1 Point-slope form
3.2 Slope-Intercept form
3.3 Two point form
3.4 Determinant form
3.5 Intercept form
3.6 Normal form
3.7 Parametric form
4.0 Angle between two lines
5.0 Length of perpendicular from a point to a line
6.0 Foot of perpendicular from a point to a line
7.0 Reflection of a point about a line
7.1 Reflection with respect to $X-$axis
7.2 Reflection with respect to $Y-$axis
7.3 Reflection with respect to Origin
7.4 Reflection with respect to the line $x=a$
7.5 Reflection with respect to the line $y=b$
7.6 Reflection with respect to the line $y=x$
8.0 Equation of angle bisector
9.0 Bisector of angle containing origin
10.0 Bisector of angle containing a given point
11.0 Family of straight lines
1.2 Slope or Gradient of a line
3.2 Slope-Intercept form
3.3 Two point form
3.4 Determinant form
3.5 Intercept form
3.6 Normal form
3.7 Parametric form
7.2 Reflection with respect to $Y-$axis
7.3 Reflection with respect to Origin
7.4 Reflection with respect to the line $x=a$
7.5 Reflection with respect to the line $y=b$
7.6 Reflection with respect to the line $y=x$
It is defined as the tangent of the inclination of the line. If the angle of inclination of a line is represented by $\theta $, then the slope or gradient of a line is given by $\tan \theta $. It is usually denoted by $m = \tan \theta $ where $\theta \ne {90^ \circ }$.
$\theta $ is positive or negative according to as it is measured in anticlockwise or clockwise direction.
From figure, $$Slope\ of\ AB = \tan \theta = \tan ( - (\pi - \theta )) = \tan (\pi + \theta ) = {\text{slope of }}BA$$
From above equation, we can say that we do not take into consideration the direction of a line segment while talking of its slope.
- If $\theta $ is ${90^ \circ }$, $m$ does not exist, but the line is parallel to $Y$-axis.
- If $\theta $ is ${0^ \circ }$, $m=0$ and line is parallel to $X$-axis.
If $A({x_1},{y_1})$ and $B({x_2},{y_2})$, ${x_1} \ne {x_2}$ are points on a straight line, then the slope $m$ of a line is given by $$m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$$
