Question

Find the slope and the inclination of the line AB if:
(i) A=(−3, −2) and B=(1, 2)

Answer 1

Finding the slope of line AB
Let, $A(-3,-2)=(x_1,y_1)$ and $B(1,2)=(x_2,y_2)$.

We know that,
Slope of line $AB=\frac{y_2-y_1}{x_2-x_1}$
$=\frac{2-(-2)}{1-(-3)}$

$=\frac{2+2}{1+3}$

$=\frac{4}{4}$

$\therefore$ Slope of line AB $=1$

Finding the inclination of line AB
Let inclination of line AB be ${\theta }^{\circ }$.
$\therefore \tan \theta =$ Slope of line AB
$\Rightarrow \tan \theta =1$
$\Rightarrow \tan \theta =\tan {45}^{\circ }$ $(\because \tan {45}^{\circ }=1)$
$\therefore \theta ={45}^{\circ }$
Hence, the slope of a line AB is $1$ and inclination is ${45}^{\circ }$.