JEE Main & Advanced Mathematics Straight Line Slope (Gradient) of a Line

The trigonometrical tangent of the angle that a line makes with the positive direction of the x-axis in anticlockwise sense is called the slope or gradient of the line. The slope of a line is generally denoted by \[m\]. Thus, \[m=\tan \theta \].

(1) Slope of line parallel to x – axis is \[m=\tan {{0}^{o}}=0\].

(2) Slope of line parallel to y – axis is \[m=\tan {{90}^{o}}=\infty \].

(3) Slope of the line equally inclined with the axes is 1 or – 1.

(4) Slope of the line through the points \[A({{x}_{1}},{{y}_{1}})\] and \[B({{x}_{2}},{{y}_{2}})\] is  \[\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\] taken in the same order.

(5) Slope of the line\[ax+by+c=0,b\ne 0\] is \[-\frac{a}{b}\].

(6) Slope of two parallel lines are equal.

(7) If \[{{m}_{1}}\] and \[{{m}_{2}}\] be the slopes of two perpendicular lines, then \[{{m}_{1}}.{{m}_{2}}=-1\].

(8) \[m\] can be defined as \[\tan \theta \] for \[0\le \theta \le \pi \] and \[\theta \ne \frac{\pi }{2}\].