The gradient measures the slope of a line. \(m=\dfrac{y_2-y_1}{x_2-x_1}=\tan\theta\qquad x_2\ne x_1\

Question

The gradient measures the slope of a line.

$m=\dfrac{y_2-y_1}{x_2-x_1}=\tan\theta\qquad x_2\ne x_1$

$\theta$ is the angle of inclination from the positive $x$-axis, $0\le\theta<\pi$. A vertical line has undefined gradient.

Vertical	Horizontal	Rising	Falling

Undefined	$0$	$m>0$	$m<0$

Keep the subtraction order the same in the numerator and denominator.

Accepted Answer

$m_{AB}=\dfrac{y_2-y_1}{x_2-x_1}=\tan\theta\text{ for }x_2\ne x_1$ $\text{vertical: undefined}$ $\text{horizontal: }m=0$ $\text{rising: }m>0$ $\text{falling: }m<0$

Gradient of a Straight Line

Gradient of a Straight Line

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