Question

Find the equation of the straight lines which cut off an intercept $4$ from the $y-$axis and are equally inclined to the axes.

Answer 1

Slope of line inclined equally to axis $=-1$

In $\Delta AOB$, $2\theta +90=180$

$\Rightarrow \theta ={45}^o$

$\Rightarrow \varphi =180-\theta ={135}^o$

$\Rightarrow$ Slope $=\tan \varphi =\tan 135=-1$

Slope $-$ intercept form,

$y=-x+4$

$\{y=mx+c\}$.